“复杂科学”的版本间的差异

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{{short description|System composed of many interacting components}}
 
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{{Redirect|Complex systems|the journal|Complex Systems (journal)}}
 
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{{Complex systems}}
 
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A '''complex system''' is a [[system]] composed of many components which may [[interaction|interact]] with each other. Examples of complex systems are Earth's global [[climate]], [[organisms]], the [[human brain]], infrastructure such as power grid, transportation or communication systems, social and economic organizations (like [[cities]]), an [[ecosystem]], a living [[Cell (biology)|cell]], and ultimately the entire [[universe]].
 
  
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Complex systems are [[system]]s whose behavior is intrinsically difficult to model due to the dependencies, competitions, relationships, or other types of interactions between their parts or between a given system and its environment. Systems that are "[[Complexity|complex]]" have distinct properties that arise from these relationships, such as [[Nonlinear system|nonlinearity]], [[emergence]], [[spontaneous order]], [[Complex adaptive system|adaptation]], and [[Feedback|feedback loops]], among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links to their interactions.
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复杂系统 complex system由许多相互作用的元素组成。复杂系统的例子无处不在：全球气候、有机体、人脑、电网、交通、通讯系统等基础设施网络、城市社会和经济组织网络、生态系统、活细胞、甚至整个宇宙，这些都可以看作是复杂系统。
  
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== Overview ==
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复杂系统是指那些本身难以直接建模的系统，因为系统组成元素之间以及系统和环境之间存在依赖、竞争、关联等复杂的相互作用。系统之所以“复杂”，是因为在这些相互作用中会产生如'''非线性 nonlinearity'''、'''涌现 emergence'''、'''自发秩序 spontaneous order''' 、'''适应性 adaptation'''以及'''反馈回路 feedback loops'''等特殊性质。因为这些系统出现在不同领域，所以对不同领域系统的共性研究慢慢发展成为一个独立的研究领域。大部分情况下，复杂系统都可以表示成一个网络，网络中的节点表示元素，连边表示相互作用。
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The term ''complex systems'' often refers to the study of complex systems, which is an approach to science that investigates how relationships between a system's parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment.<ref>{{cite journal|last=Bar-Yam|first=Yaneer|date=2002|title=General Features of Complex Systems|url=http://www.eolss.net/sample-chapters/c15/E1-29-01-00.pdf|journal=Encyclopedia of Life Support Systems|doi=|pmid=|accessdate=16 September 2014}}</ref> The study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study; for this reason, complex systems can be understood as an alternative paradigm to [[reductionism]], which attempts to explain systems in terms of their constituent parts and the individual interactions between them.
 
  
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As an interdisciplinary domain, complex systems draws contributions from many different fields, such as the study of [[self-organization]] from physics, that of [[spontaneous order]] from the social sciences, [[Chaos theory|chaos]] from mathematics, [[Complex adaptive system|adaptation]] from biology, and many others. ''Complex systems'' is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines, including [[statistical physics]], [[information theory]], [[Nonlinear system|nonlinear dynamics]], [[anthropology]], [[computer science]], [[meteorology]], [[sociology]], [[economics]], [[psychology]], and [[biology]].
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复杂系统理论是系统科学中的一个前沿方向，它是复杂性科学的主要研究任务。复杂性科学被称为21 世纪的科学，它的主要目的就是要揭示复杂系统的一些难以用现有科学方法解释的动力学行为。与传统的还原论方法不同，复杂系统理论强调用整体论和还原论相结合的方法去分析系统。目前，复杂系统理论还处于萌芽阶段，它可能蕴育着一场新的系统学乃至整个传统科学方法的革命。生命系统、社会系统都是复杂系统，复杂系统理论的应用在系统生物学的研究与生物系统计算机数学建模中具有重要的意义。
  
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== Key concepts ==
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[[File:Complex.jpeg|1500px|thumb|right|复杂系统涵盖的主题]]
  
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=== Systems ===
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== 概览 ==
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[[File:OpenSystemRepresentation.svg|thumb|252px|''Open systems'' have input and output flows, representing exchanges of matter, energy or information with their surroundings.]]
 
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Complex systems are chiefly concerned with the behaviors and properties of ''[[system]]s''. A system, broadly defined, is a set of entities that, through their interactions, relationships, or dependencies, form a unified whole. It is always defined in terms of its ''boundary'', which determines the entities that are or are not part of the system. Entities lying outside the system then become part of the system's ''environment''.
 
  
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A system can exhibit ''properties'' that produce ''behaviors'' which are distinct from the properties and behaviors of its parts; these system-wide or ''global'' properties and behaviors are characteristics of how the system interacts with or appears to its environment, or of how its parts behave (say, in response to external stimuli) by virtue of being within the system. The notion of ''behavior'' implies that the study of systems is also concerned with processes that take place over time (or, in [[mathematics]], some other [[phase space]] [[Parameter|parameterization]]). Because of their broad, interdisciplinary applicability, systems concepts play a central role in complex systems.
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'''复杂系统'''这一术语，通常是指对复杂系统的研究，表示一种新的科学研究方法。主要研究：系统元素之间的关系如何产生集体行为，系统和环境之间如何进行相互作用，将集体、系统层面的行为作为研究的基本对象<ref>Bar-Yam (2014) [https://pattern.swarma.org/paper?id=bf882316-6e74-11ea-befb-0242ac1a0005 "General Features of Complex Systems"].Yaneer, Encyclopedia of Life Support Systems. Retrieved 16 September.</ref>。因此，复杂系统可以看作是'''还原论 reductionism'''的替代范式，主要解释系统的组成部分和相互关系。
  
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As a field of study, complex system is a subset of [[systems theory]]. General systems theory focuses similarly on the collective behaviors of interacting entities, but it studies a much broader class of systems, including non-complex systems where traditional reductionist approaches may remain viable. Indeed, systems theory seeks to explore and describe ''all'' classes of systems, and the invention of categories that are useful to researchers across widely varying fields is one of the systems theory's main objectives.
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作为一个跨学科的研究领域，复杂系统吸收了许多其他领域的研究理论，如借鉴物理学对'''自组织 self-organization'''的研究，社会科学对'''自发秩序 spontaneous order'''的研究，数学对[[混沌 chaos]]的研究，生物学对'''适应性 adaptation'''的研究。因此“复杂系统”是一个宽泛的术语，涵盖了不同领域的研究方法，包括统计物理学、信息论、非线性动力学、人类学、计算机科学、气象学、社会学、经济学、心理学和生物学等。
  
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As it relates to complex systems, systems theory contributes an emphasis on the way relationships and dependencies between a system's parts can determine system-wide properties. It also contributes to the interdisciplinary perspective of the study of complex systems: the notion that shared properties link systems across disciplines, justifying the pursuit of modeling approaches applicable to complex systems wherever they appear. Specific concepts important to complex systems, such as emergence, feedback loops, and adaptation, also originate in systems theory.
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===复杂系统的共性===
  
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=== Complexity ===
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* 个人一般都遵循相对简单的规则，不存在中央控制或者领导者。
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"Systems exhibit complexity" means that their behaviors cannot be easily inferred from their properties. Any modeling approach that ignores such difficulties or characterizes them as noise, then, will necessarily produce models that are neither accurate nor useful. As yet no fully general theory of complex systems has emerged for addressing these problems, so researchers must solve them in domain-specific contexts. Researchers in complex systems address these problems by viewing the chief task of modeling to be capturing, rather than reducing, the complexity of their respective systems of interest.
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* 大量个体的集体行为产生出了复杂、不断变化而且难以预测的行为模式。
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* 利用来自内部和外部环境中的信息和信号，同时也产生信息和信号。
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* 可以通过学习和进化过程进行适应，即改变自身的行为以增加生存或成功的机会。
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'''总结'''：复杂系统由大量组分组成的网络：不存在中央控制；通过简单运作规则产生出复杂的集体行为和复杂的信息处理，并通过学习和进化产生适应性。
  
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While no generally accepted exact definition of complexity exists yet, there are many archetypal examples of complexity. Systems can be complex if, for instance, they have [[Chaos theory|chaotic]] behavior (behavior that exhibits extreme sensitivity to initial conditions), or if they have [[Emergence|emergent]] properties (properties that are not apparent from their components in isolation but which result from the relationships and dependencies they form when placed together in a system), or if they are computationally intractable to model (if they depend on a number of parameters that grows too rapidly with respect to the size of the system).
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== 重要概念 ==
  
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=== Networks ===
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=== 系统 ===
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The interacting components of a complex system form a [[Network theory|network]], which is a collection of discrete objects and relationships between them, usually depicted as a [[Graph (discrete mathematics)|graph]] of vertices connected by edges. Networks can describe the relationships between individuals within an organization, between [[logic gate]]s in a [[Circuit (computer science)|circuit]], between [[gene]]s in [[gene regulatory network]]s, or between any other set of related entities.
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[[File:OpenSystemRepresentation.svg.png|200px|thumb|right|开放系统的输入和输出流，代表系统和周围环境之间的问题、能量和信息之间的交换]]
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复杂系统主要关注的是系统的行为和性质。一个系统 system，广义地讲，是由一组实体，通过实体之间的交互、关联、或者依赖，形成一个统一的整体。系统一般由边界来定义，边界决定了哪些属于系统内的一部分，而位于系统边界之外的部分则构成了该系统的环境。一个系统可以表现出与系统个体行为和性质不一样的特性。这些系统层面（整体）的性质和特征通过系统与环境相互作用，或者由系统的部分行为体现出来（例如，对外部刺激作出反应）。此处“行为”的概念意味着，研究系统也涉及到对随时间演化的过程研究（或者，在数学中，叫做'''相空间参数化'''）。 由于其广泛的、跨学科的适用性，系统是复杂系统中极其重要的概念。
  
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Networks often describe the sources of complexity in complex systems. Studying complex systems as networks, therefore, enables many useful applications of [[graph theory]] and [[network science]]. Some complex systems, for example, are also [[complex network]]s, which have properties such as phase transitions and power-law degree distributions that readily lend themselves to emergent or chaotic behavior. The fact that the number of edges in a [[complete graph]] grows [[Quadratic growth|quadratically]] in the number of vertices sheds additional light on the source of complexity in large networks: as a network grows, the number of relationships between entities quickly dwarfs the number of entities in the network.
 
  
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=== Nonlinearity ===
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作为一个研究领域，复杂系统是系统论的一个子领域。 尽管广义的系统理论也侧重于研究相互作用实体的集体行为，但复杂系统研究的是更广泛的一类系统，包括传统还原论方法也能适用的非复杂系统。事实上，系统理论试图探索和描述所有类型的系统，主要目标就是发明对各研究领域都有用的理论。
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[[File:A Trajectory Through Phase Space in a Lorenz Attractor.gif|frame|border|right|A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8/3]]
 
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Complex systems often have nonlinear behavior, meaning they may respond in different ways to the same input depending on their state or context. In [[mathematics]] and [[physics]], nonlinearity describes systems in which a change in the size of the input does not produce a proportional change in the size of the output. For a given change in input, such systems may yield significantly greater than or less than proportional changes in output, or even no output at all, depending on the current state of the system or its parameter values.
 
  
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Of particular interest to complex systems are [[nonlinear dynamical systems]], which are systems of [[differential equation]]s that have one or more nonlinear terms. Some nonlinear dynamical systems, such as the [[Lorenz system]], can produce a mathematical phenomenon known as [[Chaos theory|chaos]]. Chaos, as it applies to complex systems, refers to the sensitive dependence on initial conditions, or "[[butterfly effect]]", that a complex system can exhibit. In such a system, small changes to initial conditions can lead to dramatically different outcomes. Chaotic behavior can, therefore, be extremely hard to model numerically, because small rounding errors at an intermediate stage of computation can cause the model to generate completely inaccurate output. Furthermore, if a complex system returns to a state similar to one it held previously, it may behave completely differently in response to the same stimuli, so chaos also poses challenges for extrapolating from experience.
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至于系统理论和复杂系统的关系，系统理论强调系统各部分之间的关系和依赖在一定程度上决定了整个系统的性质，有助于说明复杂系统的跨学科研究视角：具有共享属性的概念连接了不同领域的系统，同时证明无论是什么样的复杂系统，都可以通过建模方法对系统进行科学研究。同时复杂系统重要的特定概念，如'''涌现 emergence'''、'''反馈回路 feedback loops'''和'''适应性 adaptation'''，也起源于系统理论。
  
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=== Emergence ===
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=== 复杂性 ===
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[[File:Gospers glider gun.gif|frame|right|[[Bill Gosper|Gosper's]] [[Gun (cellular automaton)|Glider Gun]] creating "[[Glider (Conway's Life)|gliders]]" in the cellular automaton [[Conway's Game of Life]]<ref>[[Daniel Dennett]] (1995), ''[[Darwin's Dangerous Idea]]'', Penguin Books, London, {{ISBN|978-0-14-016734-4}}, {{ISBN|0-14-016734-X}}</ref>]]
 
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Another common feature of complex systems is the presence of emergent behaviors and properties: these are traits of a system that are not apparent from its components in isolation but which result from the interactions, dependencies, or relationships they form when placed together in a system. [[Emergence]] broadly describes the appearance of such behaviors and properties, and has applications to systems studied in both the social and physical sciences. While emergence is often used to refer only to the appearance of unplanned organized behavior in a complex system, emergence can also refer to the breakdown of an organization; it describes any phenomena which are difficult or even impossible to predict from the smaller entities that make up the system.
 
  
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One example of a complex system whose emergent properties have been studied extensively is [[Cellular automaton|cellular automata]]. In a cellular automaton, a grid of cells, each having one of the finitely many states, evolves according to a simple set of rules. These rules guide the "interactions" of each cell with its neighbors. Although the rules are only defined locally, they have been shown capable of producing globally interesting behavior, for example in [[Conway's Game of Life]].
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“系统表现出复杂性”意味着很难从其行为中推断出系统的性质。任何忽略这些差异和特性，或者将差异和特性视为噪声的建模方法都是不准确也没有效果的。到目前为止，还没有完全通用的复杂系统理论来解决这些问题，因此研究人员必须结合特定的领域解决问题。研究人员解决这些问题的方法是将建模的主要任务看做是刻画复杂性，而不简化系统的复杂性。
  
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==== Spontaneous order and self-organization ====
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虽然目前还没有被广泛认可的复杂性的精确定义，但是有很多关于复杂性的典型例子。例如，如果系统具有混沌行为(对初始条件表现出极度敏感的行为) ，或者如果它们具有涌现特性(这些特性从它们的组成元素中看不出来，但来源于在一个系统中产生的关系和依赖) ，或者如果它们难以计算建模(如果它们的参数数量的增加快于系统大小的增加) ，那么系统就可能是复杂的。
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When emergence describes the appearance of unplanned order, it is [[spontaneous order]] (in the social sciences) or [[self-organization]] (in physical sciences). Spontaneous order can be seen in [[herd behavior]], whereby a group of individuals coordinates their actions without centralized planning. Self-organization can be seen in the global symmetry of certain [[crystal]]s, for instance the apparent radial [[symmetry]] of [[snowflake]]s, which arises from purely local [[Intermolecular force|attractive and repulsive forces]] both between water molecules and their surrounding environment.
 
  
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=== Adaptation ===
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=== 网络 ===
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[[Complex adaptive system]]s are special cases of complex systems that are [[adaptive]] in that they have the capacity to change and learn from experience. Examples of complex adaptive systems include the [[stock market]], social insect and [[ant]] colonies, the [[biosphere]] and the [[ecosystem]], the [[Human brain|brain]] and the [[immune system]], the [[Cell (biology)|cell]] and the developing [[embryo]], the cities, [[Manufacturing|manufacturing businesses]] and any human social group-based endeavor in a cultural and [[social system]] such as [[Political party|political parties]] or [[Community|communities]].<ref>{{Cite journal | doi=10.1177/1473095218780515| title=On the 'complexity turn' in planning: An adaptive rationale to navigate spaces and times of uncertainty| year=2019| last1=Skrimizea| first1=Eirini| last2=Haniotou| first2=Helene| last3=Parra| first3=Constanza| journal=Planning Theory| volume=18| pages=122–142}}</ref>
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复杂系统中相互作用的部分组成一个网络，'''网络'''是离散对象及其相互关系的集合，通常描述为由边连接的顶点图。 网络可以描述系统中个体之间的关系，例如：电路中逻辑门之间的关系，基因调控网络中的基因之间的关系，或者任何其他相关实体之间的关系。
  
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==Features==
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网络经常用来刻画复杂系统中的复杂性。因此，把复杂系统当作网络来研究，可以使图论和[[网络科学 network science]]得到广泛应用。例如，一些复杂系统也是复杂网络，它们具有相变和幂律度分布等特性，这些特性容易导致涌现或混沌行为。一个完全图中，边的数量随着顶点数量的增加而幂次增长，这一特性进一步揭示了大型网络中复杂性的来源: 随着网络的增长，实体之间的关系增加要远快于实体数量的增加。
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Complex systems may have the following features:<ref>{{cite book|title=Risk and Precaution
 
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|author=Alan Randall
 
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|author-link=Alan Randall
 
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|isbn=9781139494793
 
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|url=https://books.google.com/books?id=IlHj3fvJzMsC&printsec=frontcover&dq=inauthor:%22Alan+Randall%22#v=onepage
 
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|publisher=Cambridge University Press|year=2011}}</ref>
 
  
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;[[Cascading failure]]s
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=== 非线性 ===
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:Due to the strong coupling between components in complex systems, a failure in one or more components can lead to cascading failures which may have catastrophic consequences on the functioning of the system.<ref>{{cite journal|author=S. V. Buldyrev|author2=R. Parshani|author3=G. Paul|author4=H. E. Stanley|author5=S. Havlin|author5-link=Shlomo Havlin|title=Catastrophic cascade of failures in interdependent networks|journal=Nature|year=2010|volume=464|pages=1025–8|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all | doi = 10.1038/nature08932|pmid=20393559|issue=7291|arxiv = 0907.1182 |bibcode = 2010Natur.464.1025B }}</ref> Localized attack may lead to cascading failures and abrupt collapse in spatial networks.<ref name="BerezinBashan2015">{{cite journal|last1=Berezin|first1=Yehiel|last2=Bashan|first2=Amir|last3=Danziger|first3=Michael M.|last4=Li|first4=Daqing|last5=Havlin|first5=Shlomo|title=Localized attacks on spatially embedded networks with dependencies|journal=Scientific Reports|volume=5|issue=1|pages=8934|year=2015|issn=2045-2322|doi=10.1038/srep08934|pmid=25757572|pmc=4355725|bibcode=2015NatSR...5E8934B}}</ref>
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[[File:A_Trajectory_Through_Phase_Space_in_a_Lorenz_Attractor.gif|200px|thumb|right|洛伦兹吸引子当 ρ = 28, σ = 10, and β = 8/3 <ref>Daniel Dennett (1995), [https://en.wikipedia.org/wiki/Darwin%27s_Dangerous_Idea Darwin's Dangerous Idea], Penguin Books, London, ISBN 978-0-14-016734-4, ISBN 0-14-016734-X </ref>]]
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复杂系统通常具有非线性行为，意味着输入相同的状态和内容，系统可能会作出不同的回应。在数学和物理学中，非线性描述的是输入和输出不成比例的系统。当给定输入变化时，系统产生的结果可能远大于或远小于输入的变化，甚至根本没有输出（这取决于系统当前的状态或参数值的取值）。
  
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;Complex systems may be open
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复杂系统中一个有意思的研究就是'''非线性动力系统'''，它是由一个或多个非线性项组成的微分方程组。一些非线性动力系统，如[[洛伦兹系统]]，可以产生一种称为'''混沌'''的数学现象。 '''混沌'''，适用于复杂系统，通常是指是指对初始条件的敏感依赖，如“蝴蝶效应” 。在这样一个系统中，小的初始改变状态可能会导致截然不同的结果。因此，混沌行为的数值模拟非常困难，因为在计算的中间阶段，很小的扰动误差会导致模型产生极为不准确的结果。此外，即使在想他刺激下，如果一个复杂的系统回到一个之前的初始状态，它可能会表现出和之前状态完全不一样的行为，完全不同的行为反应，所以混沌也对经验推断的方式提出了挑战。
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: Complex systems are usually [[Open system (systems theory)|open systems]] — that is, they exist in a [[thermodynamic]] gradient and dissipate energy. In other words, complex systems are frequently far from energetic [[thermodynamic equilibrium|equilibrium]]: but despite this flux, there may be [[pattern stability]], see [[synergetics (Haken)|synergetics]].
 
  
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;Complex systems may exhibit critical transitions
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=== 涌现 ===
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:[[Critical transition]]s are abrupt shifts in the state of [[ecosystem]]s, the [[climate]], [[financial system]]s or other complex systems that may occur when changing conditions pass a critical or [[bifurcation theory|bifurcation point]].<ref>{{cite journal |last1=Scheffer |first1=Marten |last2=Carpenter |first2=Steve |last3=Foley |first3=Jonathan A. |last4=Folke |first4=Carl |last5=Walker |first5=Brian |title=Catastrophic shifts in ecosystems |journal=Nature |date=October 2001 |volume=413 |issue=6856 |pages=591–596 |doi=10.1038/35098000 |pmid=11595939 |bibcode=2001Natur.413..591S |url=https://www.nature.com/articles/35098000 |language=en |issn=1476-4687}}</ref><ref>{{cite book |last1=Scheffer |first1=Marten |title=Critical transitions in nature and society |date=26 July 2009 |publisher=Princeton University Press |isbn=978-0691122045}}</ref><ref>{{cite journal |last1=Scheffer |first1=Marten |last2=Bascompte |first2=Jordi |last3=Brock |first3=William A. |last4=Brovkin |first4=Victor |last5=Carpenter |first5=Stephen R. |last6=Dakos |first6=Vasilis |last7=Held |first7=Hermann |last8=van Nes |first8=Egbert H. |last9=Rietkerk |first9=Max |last10=Sugihara |first10=George |title=Early-warning signals for critical transitions |journal=Nature |date=September 2009 |volume=461 |issue=7260 |pages=53–59 |doi=10.1038/nature08227 |pmid=19727193 |bibcode=2009Natur.461...53S |url=https://www.nature.com/articles/nature08227 |language=en |issn=1476-4687}}</ref><ref>{{cite journal |last1=Scheffer |first1=Marten |last2=Carpenter |first2=Stephen R. |last3=Lenton |first3=Timothy M. |last4=Bascompte |first4=Jordi |last5=Brock |first5=William |last6=Dakos |first6=Vasilis |last7=Koppel |first7=Johan van de |last8=Leemput |first8=Ingrid A. van de |last9=Levin |first9=Simon A. |last10=Nes |first10=Egbert H. van |last11=Pascual |first11=Mercedes |last12=Vandermeer |first12=John |title=Anticipating Critical Transitions |journal=Science |date=19 October 2012 |volume=338 |issue=6105 |pages=344–348 |doi=10.1126/science.1225244 |pmid=23087241 |bibcode=2012Sci...338..344S |url=https://science.sciencemag.org/content/338/6105/344 |language=en |issn=0036-8075}}</ref> The 'direction of critical slowing down' in a system's state space may be indicative of a system's future state after such transitions when delayed negative feedbacks leading to oscillatory or other complex dynamics are weak.<ref>{{cite journal |last1=Lever |first1=J. Jelle |last2=Leemput |first2=Ingrid A. |last3=Weinans |first3=Els |last4=Quax |first4=Rick |last5=Dakos |first5=Vasilis |last6=Nes |first6=Egbert H. |last7=Bascompte |first7=Jordi |last8=Scheffer |first8=Marten |title=Foreseeing the future of mutualistic communities beyond collapse |journal=Ecology Letters |volume=23 |issue=1 |pages=2–15 |doi=10.1111/ele.13401 |pmid=31707763 |pmc=6916369 |year=2020 }}</ref>
 
  
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;Complex systems may have a memory
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复杂系统的另一个共同特征是'''涌现'''行为和特性的存在：这些是系统层面的特征，无法从其组成部分中孤立地表现出来，而是由它们在系统中一起形成的相互作用、依赖或关系所形成。涌现广泛地描述了这类行为的出现，并且在社会科学和物理科学研究的系统中都有广泛应用。涌现通常是指复杂系统中出现的无计划却有组织的行为，也可以指系统的崩溃，可用于描述从组成系统的较小实体层面难以预测或无法预测的现象。
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:Recovery from a [[critical transition]] may require more than a simple return to the conditions at which a transition occurred, a phenomenon called [[hysteresis]]. The history of a complex system may thus be important. Because complex systems are [[dynamical systems]] they change over time, and prior states may have an influence on present states.<ref name="MajdandzicPodobnik2013">{{cite journal|last1=Majdandzic|first1=Antonio|last2=Podobnik|first2=Boris|last3=Buldyrev|first3=Sergey V.|last4=Kenett|first4=Dror Y.|last5=Havlin|first5=Shlomo|last6=Eugene Stanley|first6=H.|s2cid=18876614|title=Spontaneous recovery in dynamical networks|journal=Nature Physics|volume=10|issue=1|year=2013|pages=34–38|issn=1745-2473|doi=10.1038/nphys2819|bibcode=2014NatPh..10...34M|doi-access=free}}</ref> Interacting systems may have complex hysteresis of many transitions.<ref name="MajdandzicBraunstein2016">{{cite journal|last1=Majdandzic|first1=Antonio|last2=Braunstein|first2=Lidia A.|last3=Curme|first3=Chester|last4=Vodenska|first4=Irena|last5=Levy-Carciente|first5=Sary|last6=Eugene Stanley|first6=H.|last7=Havlin|first7=Shlomo|title=Multiple tipping points and optimal repairing in interacting networks|journal=Nature Communications|volume=7|year=2016|pages=10850|issn=2041-1723|doi=10.1038/ncomms10850|pmid=26926803|pmc=4773515|arxiv=1502.00244|bibcode=2016NatCo...710850M}}</ref>
 
  
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;Complex systems may be [[Hierarchy#Nested hierarchy|nested]]
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[[File: Gospers glider gun1.gif|400px|thumb| right| 康威生命游戏中出现的枪型的元胞自动机]]
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:The components of a complex system may themselves be complex systems. For example, an [[Economics|economy]] is made up of [[organisation]]s, which are made up of [[person|people]], which are made up of [[cell (biology)|cells]] - all of which are complex systems. The arrangement of interactions within complex bipartite networks may be nested as well. More specifically, bipartite ecological and organisational networks of mutually beneficial interactions were found to have a nested structure.<ref>{{cite journal |last1=Bascompte |first1=J. |last2=Jordano |first2=P. |last3=Melian |first3=C. J. |last4=Olesen |first4=J. M. |title=The nested assembly of plant-animal mutualistic networks |journal=Proceedings of the National Academy of Sciences |date=24 July 2003 |volume=100 |issue=16 |pages=9383–9387 |doi=10.1073/pnas.1633576100|pmid=12881488 |pmc=170927 |bibcode=2003PNAS..100.9383B }}</ref><ref>{{cite journal |last1=Saavedra |first1=Serguei |last2=Reed-Tsochas |first2=Felix |last3=Uzzi |first3=Brian |title=A simple model of bipartite cooperation for ecological and organizational networks |journal=Nature |date=January 2009 |volume=457 |issue=7228 |pages=463–466 |doi=10.1038/nature07532 |pmid=19052545 |bibcode=2009Natur.457..463S |language=en |issn=1476-4687}}</ref> This structure promotes indirect facilitation and a system's capacity to persist under increasingly harsh circumstances as well as the potential for large-scale systemic regime shifts.<ref>{{cite journal |last1=Bastolla |first1=Ugo |last2=Fortuna |first2=Miguel A. |last3=Pascual-García |first3=Alberto |last4=Ferrera |first4=Antonio |last5=Luque |first5=Bartolo |last6=Bascompte |first6=Jordi |title=The architecture of mutualistic networks minimizes competition and increases biodiversity |journal=Nature |date=April 2009 |volume=458 |issue=7241 |pages=1018–1020 |doi=10.1038/nature07950 |pmid=19396144 |bibcode=2009Natur.458.1018B |language=en |issn=1476-4687}}</ref><ref>{{cite journal |last1=Lever |first1=J. Jelle |last2=Nes |first2=Egbert H. van |last3=Scheffer |first3=Marten |last4=Bascompte |first4=Jordi |title=The sudden collapse of pollinator communities |journal=Ecology Letters |date=2014 |volume=17 |issue=3 |pages=350–359 |doi=10.1111/ele.12236 |pmid=24386999 |language=en |issn=1461-0248|hdl=10261/91808 |hdl-access=free }}</ref>
 
  
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;Dynamic network of multiplicity
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在复杂系统中，涌现特性被广泛研究的其中一个例子就是[[元胞自动机 Cellular Automata]]。在元胞自动机中，一个由细胞组成的网格，每个细胞都是处于某种状态，且这些状态是有限的，然后根据一组简单的规则进行演化。这些规则指导每个细胞与其邻近细胞进行“相互作用”。 尽管这些规则只是局部定义的，但是它们已经被证明能够产生全局性的有趣行为，例如'''康威的生命游戏 Conway's Game of Life'''。
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:As well as [[coupling]] rules, the dynamic [[Biological network|network]] of a complex system is important. [[Small-world network|Small-world]] or [[Scale-free network|scale-free]] networks<ref>{{cite journal|last=A. L. Barab´asi|first=R. Albert|title=Statistical mechanics of complex networks|journal=Reviews of Modern Physics |year=2002|volume=74|issue=1|pages=47–94| doi = 10.1103/RevModPhys.74.47|bibcode=2002RvMP...74...47A|arxiv = cond-mat/0106096 |citeseerx=10.1.1.242.4753}}</ref><ref>{{cite book|title= Networks: An Introduction|author= M. Newman|year=2010|publisher=Oxford University Press|isbn=978-0-19-920665-0}}</ref><ref name=":0">{{cite book|title=Complex Networks: Structure, Robustness and Function|last=Reuven Cohen|first=Shlomo Havlin|author-link=Shlomo Havlin|year=2010|publisher=Cambridge University Press|isbn=978-0-521-84156-6|title-link=Complex Networks}}</ref> which have many local interactions and a smaller number of inter-area connections are often employed. Natural complex systems often exhibit such topologies. In the human [[Cerebral cortex|cortex]] for example, we see dense local connectivity and a few very long [[axonal|axon]] projections between regions inside the cortex and to other brain regions.
 
  
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; May produce emergent phenomena
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=== 自发秩序与自组织 ===
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:Complex systems may exhibit behaviors that are [[emergence|emergent]], which is to say that while the results may be sufficiently determined by the activity of the systems' basic constituents, they may have properties that can only be studied at a higher level.  For example, the [[termites]] in a mound have physiology, biochemistry and biological development that are at one level of analysis, but their [[social behavior]] and mound building is a property that emerges from the collection of termites and needs to be analyzed at a different level.
 
  
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; Relationships are non-linear
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当涌现用于描述无计划的秩序出现时，是指自发秩序(在社会科学中)或自组织(在物理科学中)。自发秩序可以在羊群行为中看到，即一群个体在没有集中计划安排的情况下协调他们的行动；在某些晶体的整体对称性中可以看到自组织，例如雪花的径向对称性，这种对称性来自于水分子与其周围环境之间的局部吸引力和排斥力。
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: In practical terms, this means a small perturbation may cause a large effect (see [[butterfly effect]]), a proportional effect, or even no effect at all. In linear systems, the effect is ''always'' directly proportional to cause. See [[nonlinearity]].
 
  
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; Relationships contain feedback loops
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=== 适应 ===
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:Both negative ([[damping]]) and positive (amplifying) [[feedback]] are always found in complex systems. The effects of an element's behavior are fed back in such a way that the element itself is altered.
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[[复杂适应系统 Complex Adaptive Systems]]，简称CAS，是复杂系统的特例，这类系统具有改变和从经验中学习的能力，因此具有适应性。复杂适应系统的例子包括股票市场，社会昆虫，蚁群、生物圈和生态系统，大脑和免疫系统、细胞和发育中的胚胎，城市、制造业和在文化和社会系统中比如政党或者社区等人类社会群体活动。
 +
<ref name="测试">[http://journals.sagepub.com/doi/abs/10.1177/1473095218780515 On the ‘complexity turn’ in planning: An adaptive rationale to navigate spaces and times of uncertainty 关于规划中的“复杂性转向” : 一个适应性的理论基础，用于导航不确定性的空间和时间]。</ref>
  
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== History ==
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== 功能 ==
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[[File:2018 Map of the Complexity Sciences.jpg|thumb|upright=3|A perspective on the development of complexity science (see reference for readable version)<ref>[http://www.art-sciencefactory.com/complexity-map_feb09.html Castellani, Brian, 2018, ''Map of the Complexity Sciences'' Art & Science Factory (expandable version)]</ref>]]
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复杂系统可能具有以下特征<ref >Alan Randall (2011). [https://books.google.com/?id=IlHj3fvJzMsC&printsec=frontcover&dq=inauthor:%22Alan+Randall%22#v=onepage&q&f=false Risk and Precaution]. Cambridge University Press. ISBN 9781139494793.</ref>：
  
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Although arguably, humans have been studying complex systems for thousands of years, the modern scientific study of complex systems is relatively young in comparison to established fields of science such as [[physics]] and [[chemistry]]. The history of the scientific study of these systems follows several different research trends.
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'''级联失效'''
  
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In the area of [[mathematics]], arguably the largest contribution to the study of complex systems was the discovery of [[chaos theory|chaos]] in [[deterministic]] systems, a feature of certain [[dynamical systems]] that is strongly related to [[nonlinearity]].<ref>[http://www.irit.fr/COSI/training/complexity-tutorial/history-of-complex-systems.htm History of Complex Systems<!-- Bot generated title -->] {{webarchive|url=https://web.archive.org/web/20071123171158/http://www.irit.fr/COSI/training/complexity-tutorial/history-of-complex-systems.htm |date=2007-11-23 }}</ref> The study of [[neural networks]] was also integral in advancing the mathematics needed to study complex systems.
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由于复杂系统中组成部分之间的强耦合性，一个或多个组成部分的失效可能导致级联失效，这可能对系统的运行造成灾难性的后果<ref>S. V. Buldyrev; R. Parshani; G. Paul; H. E. Stanley; S. Havlin (2010). [http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all "Catastrophic cascade of failures in interdependent networks"]. Nature. 464 (7291): 1025–8. arXiv:0907.1182. Bibcode:2010Natur.464.1025B. doi:10.1038/nature08932. PMID 20393559</ref>。局部攻击可能导致空间网络的级联失效或突然崩溃。<ref>Berezin, Yehiel; Bashan, Amir; Danziger, Michael M.; Li, Daqing; Havlin, Shlomo (2015). [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4355725 "Localized attacks on spatially embedded networks with dependencies"]. Scientific Reports. 5 (1): 8934. Bibcode:2015NatSR...5E8934B. doi:10.1038/srep08934. ISSN 2045-2322. PMC 4355725. PMID 25757572</ref>
  
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The notion of [[self-organizing]] systems is tied with work in [[nonequilibrium thermodynamics]], including that pioneered by [[chemist]] and [[Nobel laureate]] [[Ilya Prigogine]] in his study of [[dissipative structures]]. Even older is the work by [[Hartree-Fock]] on the [[quantum chemistry]] equations and later calculations of the structure of molecules which can be regarded as one of the earliest examples of emergence and emergent wholes in science.
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'''开放系统'''
  
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One complex system containing humans is the classical political economy of the [[Scottish Enlightenment]], later developed by the [[Austrian school of economics]], which argues that order in market systems is spontaneous (or [[Emergence|emergent]]) in that it is the result of human action, but not the execution of any human design.<ref>{{cite book |last=Ferguson |first=Adam |authorlink=Adam Ferguson |title=An Essay on the History of Civil Society |publisher=T. Cadell |year=1767 |location=London |pages=Part the Third, Section II, p. 205 |url=http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=1428&Itemid=28 |doi= |id= |isbn= |nopp=true}}</ref><ref>Friedrich Hayek, "The Results of Human Action but Not of Human Design" in ''New Studies in Philosophy, Politics, Economics'', Chicago: University of Chicago Press, 1978, pp. 96–105.</ref>
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复杂系统通常是开放系统，即存在热力学梯度和耗散能量。换句话说，复杂系统经常远离能量平衡态: 但是尽管存在这种变动，仍然可能存在稳定的模式，参见[[协同作用 synergetics]]。
  
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Upon this, the Austrian school developed from the 19th to the early 20th century the [[economic calculation problem]], along with the concept of [[dispersed knowledge]], which were to fuel debates against the then-dominant [[Keynesian economics]]. This debate would notably lead economists, politicians, and other parties to explore the question of [[Economic calculation problem#Computational complexity|computational complexity]].{{Citation needed|date=November 2016}}
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'''系统演化'''
  
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A pioneer in the field, and inspired by [[Karl Popper]]'s and [[Warren Weaver]]'s works, Nobel prize economist and philosopher [[Friedrich Hayek]] dedicated much of his work, from early to the late 20th century, to the study of complex phenomena,<ref>Bruce J. Caldwell, Popper and Hayek: [http://www.unites.uqam.ca/philo/pdf/Caldwell_2003-01.pdf Who influenced whom?] {{Webarchive|url=https://web.archive.org/web/20181211175441/https://unites.uqam.ca/philo/pdf/Caldwell_2003-01.pdf |date=2018-12-11 }}, Karl Popper 2002 Centenary Congress, 2002.</ref> not constraining his work to human economies but venturing into other fields such as [[psychology]],<ref>Friedrich von Hayek, ''[https://archive.org/details/sensoryorderinqu00haye <!-- quote="The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology". --> The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology]'', The University of Chicago Press, 1952.</ref> [[biology]] and [[cybernetics]]. [[Gregory Bateson]] played a key role in establishing the connection between anthropology and systems theory; he recognized that the interactive parts of cultures function much like ecosystems.
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一个系统的演化过程可能是非常重要的，因为复杂系统是随着时间演化的动力系统，历史状态可能对当前状态有影响。 更正式地说，复杂系统往往表现出'''自发故障 spontaneous failures'''、'''恢复 recovery''' 以及'''磁滞 hysteresis'''。<ref name="a">Majdandzic, Antonio; Podobnik, Boris; Buldyrev, Sergey V.; Kenett, Dror Y.; Havlin, Shlomo; Eugene Stanley, H. (2013). [https://semanticscholar.org/paper/61d27eb74b6e401852d434a75aad05fe52c7c4a5 "Spontaneous recovery in dynamical networks"]. Nature Physics. 10 (1): 34–38. Bibcode:2014NatPh..10...34M. doi:10.1038/nphys2819. ISSN 1745-2473.</ref>。 当延迟的负反馈导致振荡或其他复杂动力学变弱时<ref >Lever, J. Jelle; Leemput, Ingrid A.; Weinans, Els; Quax, Rick; Dakos, Vasilis; Nes, Egbert H.; Bascompte, Jordi; Scheffer, Marten (10 November 2019). "Foreseeing the future of mutualistic communities beyond collapse". Ecology Letters. doi:10.1111/ele.13401. PMID 31707763.</ref>，系统状态空间中的“临界减速方向”可能预示着系统在这种“临界转换”之后的未来状态。相互作用系统可能具有许多相变的复杂滞后现象。<ref name="9a">Majdandzic, Antonio; Braunstein, Lidia A.; Curme, Chester; Vodenska, Irena; Levy-Carciente, Sary; Eugene Stanley, H.; Havlin, Shlomo (2016). [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4773515 "Multiple tipping points and optimal repairing in interacting networks". ]Nature Communications. 7: 10850. arXiv:1502.00244. Bibcode:2016NatCo...710850M. doi:10.1038/ncomms10850. ISSN 2041-1723. PMC 4773515. PMID 26926803.</ref>
  
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While the explicit study of complex systems dates at least to the 1970s,<ref>{{cite book |last=Vemuri |first=V. |date=1978 |title=Modeling of Complex Systems: An Introduction |location=New York |publisher=Academic Press|isbn=978-0127165509}}</ref> the first research institute focused on complex systems, the [[Santa Fe Institute]], was founded in 1984.<ref>{{cite journal | last1 = Ledford | first1 = H | year = 2015 | title = How to solve the world's biggest problems | journal = Nature | volume = 525 | issue = 7569| pages = 308–311 | doi=10.1038/525308a| pmid = 26381968 | bibcode = 2015Natur.525..308L | doi-access = free }}</ref><ref>{{Cite web|url=https://www.santafe.edu/about/history|title=History {{!}} Santa Fe Institute|website=www.santafe.edu|language=en|access-date=2018-05-17}}</ref> Early Santa Fe Institute participants included physics Nobel laureates [[Murray Gell-Mann]] and [[Philip Warren Anderson|Philip Anderson]], economics Nobel laureate [[Kenneth Arrow]], and Manhattan Project scientists [[George Cowan]] and [[Herbert L. Anderson|Herb Anderson]].<ref>Waldrop, M. M. (1993). [https://archive.org/details/complexity00mmit Complexity: The emerging science at the edge of order and chaos.] Simon and Schuster.</ref> Today, there are over 50 [[#Institutes_and_research_centers|institutes and research centers]] focusing on complex systems.{{citation needed|date=April 2019}}
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'''系统嵌套'''
  
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== Applications ==
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复杂系统的组成部分也可能是一个复杂系统。 例如，一个经济体是由组织构成的，这些组织是由人构成的，这些人是由细胞构成的——而所有这些（经济体、组织、人、细胞）都可以看作是复杂系统。 在复杂的二分网络中，相互作用的排列也可以是嵌套的。 更具体地说，互相进行有益交互的二分生态和组织网络被发现具有嵌套结构。<ref >Bascompte, J.; Jordano, P.; Melian, C. J.; Olesen, J. M. (24 July 2003). [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC170927 "The nested assembly of plant-animal mutualistic networks".] Proceedings of the National Academy of Sciences. 100 (16): 9383–9387. doi:10.1073/pnas.1633576100. PMC 170927. PMID 12881488. </ref> <ref >Saavedra, Serguei; Reed-Tsochas, Felix; Uzzi, Brian (January 2009). "A simple model of bipartite cooperation for ecological and organizational networks". Nature. 457 (7228): 463–466. doi:10.1038/nature07532. ISSN 1476-4687. PMID 19052545. </ref> 这种结构提高了间接促进作用和系统在日益严峻的环境下持续存在的能力，以及大规模系统性政权转移的可能性。<ref >Bastolla, Ugo; Fortuna, Miguel A.; Pascual-García, Alberto; Ferrera, Antonio; Luque, Bartolo; Bascompte, Jordi (April 2009). "The architecture of mutualistic networks minimizes competition and increases biodiversity". Nature. 458 (7241): 1018–1020. doi:10.1038/nature07950. ISSN 1476-4687. PMID 19396144. </ref> <ref >Lever, J. Jelle; Nes, Egbert H. van; Scheffer, Marten; Bascompte, Jordi (2014). "The sudden collapse of pollinator communities". Ecology Letters. 17 (3): 350–359. doi:10.1111/ele.12236. hdl:10261/91808. ISSN 1461-0248. PMID 24386999.</ref>
  
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===Complexity in practice===
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'''网络动力学多样性'''
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The traditional approach to dealing with complexity is to reduce or constrain it. Typically, this involves compartmentalization: dividing a large system into separate parts. Organizations, for instance, divide their work into departments that each deal with separate issues. Engineering systems are often designed using modular components. However, modular designs become susceptible to failure when issues arise that bridge the divisions.
 
  
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===Complexity management===
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除了有耦合规则，复杂系统的网络动力学也是非常重要的。局部相互作用以及少数优先连接在'''小世界网络'''或'''无标度网络'''<ref>A. L. Barab´asi, R. Albert (2002). "Statistical mechanics of complex networks". Reviews of Modern Physics. 74 (1): 47–94. arXiv:cond-mat/0106096. Bibcode:2002RvMP...74...47A. CiteSeerX 10.1.1.242.4753. doi:10.1103/RevModPhys.74.47 </ref><ref>M. Newman (2010). Networks: An Introduction. Oxford University Press. ISBN 978-0-19-920665-0.</ref><ref name="c">Reuven Cohen, Shlomo Havlin (2010).[https://en.wikipedia.org/wiki/Complex_Networks Complex Networks: Structure, Robustness and Function. ]Cambridge University Press. ISBN 978-0-521-84156-6.</ref>经常被应用，特别是自然复杂系统经常表现出这样的拓扑结构。 例如，在人类的大脑皮层，我们可以看到密集的局部连接，以及一些非常长的轴突在大脑皮层内部和其他大脑区域之间的投射。
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As projects and [[acquisitions]] become increasingly complex, companies and governments are challenged to find effective ways to manage mega-acquisitions such as the Army [[Future Combat Systems]]. Acquisitions such as the [[Future Combat Systems|FCS]] rely on a web of interrelated parts which interact unpredictably. As acquisitions become more network-centric and complex, businesses will be forced to find ways to manage complexity while governments will be challenged to provide effective governance to ensure flexibility and resiliency.<ref>[http://csis.org/files/publication/090410_Organizing_for_a_Complex_World_The_Way_Ahead_0.pdf CSIS paper: "Organizing for a Complex World: The Way Ahead]</ref>
 
  
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===Complexity economics===
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'''涌现现象的产生'''
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Over the last decades, within the emerging field of [[complexity economics]], new predictive tools have been developed to explain economic growth. Such is the case with the models built by the [[Santa Fe Institute]] in 1989 and the more recent [[economic complexity index]] (ECI), introduced by the [[MIT]] physicist [[Cesar A. Hidalgo]] and the [[Harvard]] economist [[Ricardo Hausmann]]. Based on the ECI, Hausmann, Hidalgo and their team of [[The Observatory of Economic Complexity]] have [[List of countries by future GDP (based on ECI) estimates|produced GDP forecasts for the year 2020]].{{Citation needed|date=February 2016}}
 
  
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=== Complexity and education ===
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复杂系统很多行为都是涌现的。也就是说，虽然结果可能由系统的基本组成部分的活动决定的，但它们需要从更高的层次进行研究分析。 例如，在蚁丘中的白蚁具有生理学特征、生物化学特征和生物学的发育特征，这些都处于一个分析层面的，但是它们的社会行为和蚁丘的建造是白蚁集体层面涌现出来的属性，需要在不同的层面上进行分析。
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Focusing on issues of student persistence with their studies, Forsman, Moll and Linder explore the "viability of using complexity science as a frame to extend methodological applications for physics education research", finding that "framing a social network analysis within a complexity science perspective offers a new and powerful applicability across a broad range of PER topics".<ref>{{Cite journal|last1=Forsman|first1=Jonas|last2=Moll|first2=Rachel|last3=Linder|first3=Cedric|date=2014|title=Extending the theoretical framing for physics education research: An illustrative application of complexity science|journal=Physical Review Special Topics: Physics Education Research|volume=10|issue=2|pages=020122|doi=10.1103/PhysRevSTPER.10.020122|hdl=10613/2583|bibcode=2014PRPER..10b0122F|doi-access=free}}</ref>
 
  
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===Complexity and modeling===
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'''非线性关系'''
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One of Friedrich Hayek's main contributions to early complexity theory is his distinction between the human capacity to predict the behavior of simple systems and its capacity to predict the behavior of complex systems through [[Scientific modelling|modeling]]. He believed that economics and the sciences of complex phenomena in general, which in his view included biology, psychology, and so on, could not be modeled after the sciences that deal with essentially simple phenomena like physics.<ref>{{Cite web |url=http://www.reason.com/news/show/33304.html |title=Reason Magazine - The Road from Serfdom<!-- Bot generated title --> |access-date=2017-09-22 |archive-url=https://web.archive.org/web/20070310040317/http://www.reason.com/news/show/33304.html |archive-date=2007-03-10 |url-status=dead }}</ref> Hayek would notably explain that complex phenomena, through modeling, can only allow pattern predictions, compared with the precise predictions that can be made out of non-complex phenomena.<ref>[http://nobelprize.org/nobel_prizes/economics/laureates/1974/hayek-lecture.html Friedrich August von Hayek - Prize Lecture<!-- Bot generated title -->]</ref>
 
  
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===Complexity and chaos theory===
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实际上，这意味着一个小的扰动可能会引发大的效应(见[[蝴蝶效应 butterfly effect]]) 或者一个成比例的效应或者甚至根本没有效应。 在线性系统中，效应总是与输入成比例。 而非线性 nonlinearity则相反。
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Complexity theory is rooted in [[chaos theory]], which in turn has its origins more than a century ago in the work of the French mathematician [[Henri Poincaré]]. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order.<ref>Hayles, N. K. (1991). ''[https://books.google.com/books?hl=en&lr=&id=9g9QDwAAQBAJ&oi=fnd&pg=PR7&dq=%22Chaos+Bound:+Orderly+Disorder+in+Contemporary+Literature+and+science%22&ots=1YiHUgn5wY&sig=sKu7-CerpexzdUT6o-PhVk_Ld9U#v=onepage&q=%22Chaos%20Bound%3A%20Orderly%20Disorder%20in%20Contemporary%20Literature%20and%20science%22&f=false Chaos Bound: Orderly Disorder in Contemporary Literature and Science]''. Cornell University Press, Ithaca, NY.</ref> Chaotic systems remain deterministic, though their long-term behavior can be difficult to predict with any accuracy. With perfect knowledge of the initial conditions and the relevant equations describing the chaotic system's behavior, one can theoretically make perfectly accurate predictions of the system, though in practice this is impossible to do with arbitrary accuracy. [[Ilya Prigogine]] argued<ref>Prigogine, I. (1997). ''The End of Certainty'', The Free Press, New York.</ref> that complexity is non-deterministic and gives no way whatsoever to precisely predict the future.<ref>See also {{cite journal |author=D. Carfì |year=2008 |title=Superpositions in Prigogine approach to irreversibility |journal=AAPP: Physical, Mathematical, and Natural Sciences |volume=86 |issue=1 |pages=1–13 |url=http://cab.unime.it/journals/index.php/AAPP/article/view/384/0 |format= |accessdate=}}.</ref>
 
  
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The emergence of complexity theory shows a domain between deterministic order and randomness which is complex.<ref name="PC98">[[Paul Cilliers|Cilliers, P.]] (1998). ''Complexity and Postmodernism: Understanding Complex Systems'', Routledge, London.</ref> This is referred to as the "[[edge of chaos]]".<ref>[[Per Bak]] (1996). ''How Nature Works: The Science of Self-Organized Criticality'', Copernicus, New York, U.S.</ref>
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'''反馈循环'''
  
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[[File:Lorenz attractor yb.svg|thumb|left|200px|A plot of the [[Lorenz attractor]].]]
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在复杂系统中，经常会存在负反馈和正反馈。 元素行为的影响以元素本身被改变的方式反馈到系统中。
  
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When one analyzes complex systems, sensitivity to initial conditions, for example, is not an issue as important as it is within chaos theory, in which it prevails. As stated by Colander,<ref>Colander, D. (2000). ''The Complexity Vision and the Teaching of Economics'', E. Elgar, Northampton, Massachusetts.</ref> the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioral patterns, whereas chaotic behavior, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions.<ref name="PC98"/>
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== 历史 ==
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[[File:2018 Map of the Complexity Sciences.jpg|thumb|upright=3|复杂性科学发展地图<ref>[http://www.art-sciencefactory.com/complexity-map_feb09.html Castellani, Brian, 2018, ''Map of the Complexity Sciences'' Art & Science Factory (expandable version)]</ref>]]
  
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Therefore, the main difference between chaotic systems and complex systems is their history.<ref> Buchanan, M. (2000). ''Ubiquity : Why catastrophes happen'', three river press, New-York.</ref> Chaotic systems do not rely on their history as complex ones do. Chaotic behavior pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'.{{clarify|date=September 2011}} On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events, which physicist [[Murray Gell-Mann]] called "an accumulation of frozen accidents".<ref>Gell-Mann, M. (1995). What is Complexity?  Complexity 1/1, 16-19</ref> In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations.
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可以说，人类研究复杂系统已有数千年的历史，但与物理和化学等已确立的科学领域相比，复杂系统的现代科学研究还相对年轻。 系统科学的研究历史和几种不同的研究趋势有关。
  
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{{clear left}}
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在数学领域，可以说对复杂系统研究的最大贡献是发现了确定性系统中[[混沌 chaos]]现象，在某些特定的动力系统有一个重要的特征也与数学有关，即[[非线性 nonlinearity]]。<ref>[http://www.irit.fr/COSI/training/complexity-tutorial/history-of-complex-systems.htm History of Complex Systems] Archived 2007-11-23 at the 2007-11-23Wayback Machine</ref>神经网络研究的数学部分在推进复杂系统的研究中也是不可或缺的。
  
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===Complexity and network science===
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自组织系统的概念与非平衡热力学中的研究有关，化学先驱和诺贝尔奖获得者伊利亚 · 普里高金 Ilya Prigogine在他的[[耗散结构 dissipative structures]]研究中首次提到这个概念。 更久远的可以追溯到 Hartree-Fock关于量子化学方程的工作，以及后来对分子结构的计算，这些可以被看作是科学上涌现和整体涌现最早的例子之一。
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A complex system is usually composed of many components and their interactions. Such a system can be represented by a network where nodes represent the components and links represent their interactions.<ref name=":0" /><ref name="DorogovtsevMendes2003">{{cite book|last1=Dorogovtsev|first1=S.N.|last2=Mendes|first2=J.F.F.|year=2003|doi=10.1093/acprof:oso/9780198515906.001.0001|title=Evolution of Networks|journal=Adv. Phys.|volume=51|pages=1079|arxiv=cond-mat/0106144|isbn=9780198515906}}</ref>
 
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<ref name="Fortunato2011">{{cite journal|last1=Fortunato|first1=Santo|title=Reuven Cohen and Shlomo Havlin: Complex Networks|journal=Journal of Statistical Physics|volume=142|issue=3|year=2011|pages=640–641|issn=0022-4715|doi=10.1007/s10955-011-0129-7|bibcode=2011JSP...142..640F}}</ref><ref name="Newman2010">{{cite book|last1=Newman|first1=Mark|year=2010|doi=10.1093/acprof:oso/9780199206650.001.0001|title=Networks|isbn=9780199206650|url=http://cds.cern.ch/record/1281254}}</ref> For example, the internet can be represented as a network composed of nodes (computers) and links (direct connections between computers). Its resilience to failures was studied using percolation theory.<ref name="CohenErez2001">{{cite journal|last1=Cohen|first1=Reuven|last2=Erez|first2=Keren|last3=ben-Avraham|first3=Daniel|last4=Havlin|first4=Shlomo|title=Cohen, Erez, ben-Avraham, and Havlin Reply|journal=Physical Review Letters|volume=87|issue=21|pages=219802|year=2001|issn=0031-9007|doi=10.1103/PhysRevLett.87.219802|bibcode=2001PhRvL..87u9802C}}</ref>
 
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Other examples are social networks, airline networks,<ref name="BarratBarthelemy2004">{{cite journal|last1=Barrat|first1=A.|last2=Barthelemy|first2=M.|last3=Pastor-Satorras|first3=R.|last4=Vespignani|first4=A.|title=The architecture of complex weighted networks|journal=Proceedings of the National Academy of Sciences|volume=101|issue=11|year=2004|pages=3747–3752|issn=0027-8424|doi=10.1073/pnas.0400087101|pmid=15007165|pmc=374315|arxiv=cond-mat/0311416|bibcode=2004PNAS..101.3747B}}</ref> biological networks and climate networks.<ref name="YamasakiGozolchiani2008">{{cite journal|last1=Yamasaki|first1=K.|last2=Gozolchiani|first2=A.|last3=Havlin|first3=S.|s2cid=9268697|title=Climate Networks around the Globe are Significantly Affected by El Niño|journal=Physical Review Letters|volume=100|issue=22|year=2008|issn=0031-9007|doi=10.1103/PhysRevLett.100.228501|pmid=18643467|page=228501|bibcode=2008PhRvL.100v8501Y}}</ref>
 
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Networks can also fail and recover spontaneously. For modeling this phenomenon see Majdandzic et al.<ref name="MajdandzicPodobnik2013"/>
 
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Interacting complex systems can be modeled as networks of networks. For their breakdown and recovery properties see Gao et al.<ref name="GaoBuldyrev2011">{{cite journal|last1=Gao|first1=Jianxi|last2=Buldyrev|first2=Sergey V.|last3=Stanley|first3=H. Eugene|last4=Havlin|first4=Shlomo|title=Networks formed from interdependent networks|journal=Nature Physics|volume=8|issue=1|year=2011|pages=40–48|issn=1745-2473|doi=10.1038/nphys2180|bibcode=2012NatPh...8...40G|url=http://cps-www.bu.edu/hes/articles/gbsh12.pdf|citeseerx=10.1.1.379.8214}}</ref>
 
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<ref name="MajdandzicBraunstein2016"/> Traffic in a city can be represented as a network. The weighted links represent the velocity between two junctions (nodes). This approach was found useful to characterize the global traffic efficiency in a city.<ref>{{Cite journal|last1=Li|first1=Daqing|last2=Fu|first2=Bowen|last3=Wang|first3=Yunpeng|last4=Lu|first4=Guangquan|last5=Berezin|first5=Yehiel|last6=Stanley|first6=H. Eugene|last7=Havlin|first7=Shlomo|date=2015-01-20|title=Percolation transition in dynamical traffic network with evolving critical bottlenecks|journal=Proceedings of the National Academy of Sciences|language=en|volume=112|issue=3|pages=669–672|doi=10.1073/pnas.1419185112|issn=0027-8424|pmid=25552558|bibcode=2015PNAS..112..669L|pmc=4311803}}</ref> For a quantitative definition of resilience in traffic and other infrastructure systems see <ref>{{Cite journal|last1=Limiao Zhang|first1= Guanwen Zeng|last2=Daqing Li|first2=Hai-Jun Huang|last3=H Eugene Stanley|first3=Shlomo Havlin|date=2019|title=Scale-free resilience of real traffic jams|journal=Proceedings of the National Academy of Sciences|language=en|volume=116|issue=18|pages=8673–8678|doi= 10.1073/pnas.1814982116 |arxiv=1804.11047|pmid= 30979803|bibcode=2019PNAS..116.8673Z |pmc=6500150}}</ref>
 
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The complex pattern of exposures between financial institutions has been shown to trigger financial instability.<ref>{{Cite journal|last1=Battiston|first1= Stefano|last2=Caldarelli|first2=Guido|last3=May|first3=Robert M.|last4=Roukny|first4=tarik|last5=Stiglitz|first5=Joseph E.|date=2016-09-06|title=The price of complexity in financial networks|journal=Proceedings of the National Academy of Sciences|language=en|volume=113|issue=36|pages=10031–10036|doi=10.1073/pnas.1521573113|pmid= 27555583|bibcode=2016PNAS..11310031B|pmc=5018742}}</ref>
 
  
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===General form of complexity computation===
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苏格兰启蒙运动的古典政治经济学是一个考虑人类在内的复杂系统，后来由奥地利经济学派发展，其认为市场系统的秩序是自发的(或涌现的) ，因为它是人类行为的结果，而不是任何人类设计的执行。<ref>Ferguson, Adam (1767). [http://oll.libertyfund.org/index.php?option=com_staticxt&staticfile=show.php%3Ftitle=1428&Itemid=28 An Essay on the History of Civil Society. ]London: T. Cadell. Part the Third, Section II, p. 205.</ref><ref>Friedrich Hayek, "The Results of Human Action but Not of Human Design" in New Studies in Philosophy, Politics, Economics, Chicago: University of Chicago Press, 1978, pp. 96–105.</ref>
  
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The computational law of reachable optimality<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 4.</ref> is established as a general form of computation for ordered systems and it reveals complexity computation is a compound computation of optimal choice and optimality driven reaching pattern over time underlying a specific and any experience path of an ordered system within the general limitation of system integrity.
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在此基础上，奥地利学派从19世纪到20世纪发展了早期的'''经济计算 economic calculation problem'''问题，随后提出了'''分散知识 dispersed knowledge'''的概念（即没有一个单一的行为主体拥有影响整个系统的价格和生产的所有因素的信息），这一概念引发了对当时占主导地位的凯恩斯主义的争论。 这场争论引起了经济学家、政治家和其他政党对计算复杂性问题的关注。
  
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The computational law of reachable optimality has four key components as described below.
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诺贝尔经济学奖得主、哲学家'''弗里德里希·哈耶克 F. A. Hayek'''是这一领域的先驱，受到卡尔•波普尔 Karl Popper和沃伦•韦弗 Warren Weaver 著作的启发，从20世纪早期到晚期，他的大部分工作致力于研究复杂现象<ref>Bruce J. Caldwell, Popper and Hayek:[http://www.unites.uqam.ca/philo/pdf/Caldwell_2003-01.pdf Who influenced whom? ]Archived 2018-12-11 at the Wayback Machine, Karl Popper 2002 Centenary Congress, 2002.</ref>，但他不是将他的工作局限于人类经济，而是涉足心理学<ref>Friedrich von Hayek, [https://books.google.com/books?hl=en&lr=&id=UFazm1Xy_j4C&oi=fnd&pg=PR6&dq=%22The+Sensory+Order:+An+Inquiry+into+the+Foundations+of+Theoretical+Psychology%22&ots=8NaQUtniMV&sig=lTTE8F-D3uiLGW7Yya5_1Q4i80w#v=onepage&q=%22The%20Sensory%20Order%3A%20An%20Inquiry%20into%20the%20Foundations%20of%20Theoretical%20Psychology%22&f=false The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology], The University of Chicago Press, 1952.</ref>、生物学和控制论等其他领域。
  
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1. '''Reachability of Optimality''': Any intended optimality shall be reachable. Unreachable optimality has no meaning for a member in the ordered system and even for the ordered system itself.
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此外'''格雷戈里 · 贝特森 Gregory Bateson'''在建立人类学和系统论之间的联系方面发挥了关键作用：他指出文化的互动部分很像生态系统。
  
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2. '''Prevailing and Consistency''': Maximizing reachability to explore best available optimality is the prevailing computation logic for all members in the ordered system and is accommodated by the ordered system.
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虽然对复杂系统的明确研究至少可以追溯到20世纪70年代<ref>Vemuri, V. (1978). Modeling of Complex Systems: An Introduction. New York: Academic Press. ISBN 978-0127165509.</ref>，但第一个专注于复杂系统的研究机构是[[圣塔菲研究所]] Santa Fe Institute，成立于1984年<ref>Ledford, H (2015). "How to solve the world's biggest problems". Nature. 525 (7569): 308–311. Bibcode:2015Natur.525..308L. doi:10.1038/525308a. PMID 26381968.</ref><ref>[https://www.santafe.edu/about/history "History | Santa Fe Institute"]. www.santafe.edu. Retrieved 2018-05-17.</ref>。 圣菲研究所的早期参与者包括诺贝尔物理学奖得主默里·盖尔曼 Murray Gell-Mann和 菲利普·安德森 Philip Anderson，诺贝尔经济学奖得主 肯尼思·阿诺 Kenneth Arrow，以及曼哈顿计划的科学家乔治·考温 George Cowan 和 赫伯·安德森 Herb Anderson<ref>Waldrop, M. M. (1993). [https://books.google.com/books/about/Complexity.html?id=JTRJxYK_tZsC Complexity: The emerging science at the edge of order and chaos]. Simon and Schuster.</ref>。到现在已经有50多个专注于复杂系统研究所和研究中心。
  
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3. '''Conditionality''': Realizable tradeoff between reachability and optimality depends primarily upon the initial bet capacity and how the bet capacity evolves along with the payoff table update path triggered by bet behavior and empowered by the underlying law of reward and punishment. Precisely, it is a sequence of conditional events where the next event happens upon reached status quo from experience path.
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== 应用 ==
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=== 实践中的复杂性 ===
  
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4. '''Robustness''': The more challenge a reachable optimality can accommodate, the more robust it is in terms of path integrity.
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传统的处理复杂性的方法是减少或限制的方式。通常情况下，这涉及到'''部门化 compartmentalization''': 将一个大的系统划分成独立的部分。 例如，组织将他们的工作分成不同的部门，每个部门处理不同的问题。 工程系统设计通常采用模块化组件。 然而，当部门之间的连接出现问题时，模块化设计很容易失败。
  
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There are also four computation features in the law of reachable optimality.
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=== 复杂性管理 ===
  
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1. '''Optimal Choice''': Computation in realizing Optimal Choice can be very simple or very complex. A simple rule in Optimal Choice is to accept whatever is reached, Reward As You Go (RAYG). A Reachable Optimality computation reduces into optimizing reachability when RAYG is adopted. The Optimal Choice computation can be more complex when multiple NE strategies present in a reached game.
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随着项目和收购变得越来越复杂，公司和政府面临着挑战去找到有效方法来管理大型收购，例如：陆军未来战斗系统（FCS）。FCS收购依赖于相互关联的部分，而它们之间的相互作用是无法预测的，随着收购变得越来越以网络为中心和复杂化，企业将被迫设法管理复杂性，而政府将面临挑战去提供有效治理，以确保灵活性和韧性 resiliency。<ref>[http://csis.org/files/publication/090410_Organizing_for_a_Complex_World_The_Way_Ahead_0.pdf CSIS paper: "Organizing for a Complex World: The Way Ahead]</ref>
  
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2. '''Initial Status''': Computation is assumed to start at an interesting beginning even the absolute beginning of an ordered system in nature may not and need not present. An assumed neutral Initial Status facilitates an artificial or a simulating computation and is not expected to change the prevalence of any findings.
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=== 复杂经济学 ===
  
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3. '''Territory''': An ordered system shall have a territory where the universal computation sponsored by the system will produce an optimal solution still within the territory.
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在过去的几十年里，在复杂经济学 complexity ecomomics的新兴领域中，新的预测模型已经被开发出来，用于解释经济增长。比如1989年由圣菲研究所建立的模型（人工股票市场模型），以及最近由麻省理工学院物理学家塞萨尔·伊达尔戈 César A. Hidalgo和哈佛大学经济学家 里卡多 · 豪斯曼 Ricardo Hausmann 提出的经济复杂性指数 economic complexity index 。基于ECI指数 Economic Complexity Index，Hausmann、Hidalgo 和他们的经济复杂性观测站团队已经做出了2020年的 GDP 预测。
  
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4. '''Reaching Pattern''': The forms of Reaching Pattern in the computation space, or the Optimality Driven Reaching Pattern in the computation space, primarily depend upon the nature and dimensions of measure space underlying a computation space and the law of punishment and reward underlying the realized experience path of reaching. There are five basic forms of experience path we are interested in, persistently positive reinforcement experience path, persistently [[negative reinforcement]] experience path, mixed persistent pattern experience path, decaying scale experience path and selection experience path.
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=== 复杂性与教育 ===
  
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The compound computation in the selection experience path includes current and lagging interaction, dynamic topological transformation and implies both invariance and variance characteristics in an ordered system's experience path.
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福斯曼 Forsman、莫尔 Moll 和林德 Linder关注学生持续学习的问题，探讨了“将复杂性科学作为一个框架来扩展物理教育研究 physics education research法应用的可行性” ，发现“在复杂性科学的视角内构建社会网络分析，为广泛的物理教育研究PER主题提供了新的强大的适用性”。 <ref > Forsman, Jonas; Moll, Rachel; Linder, Cedric (2014). "Extending the theoretical framing for physics education research: An illustrative application of complexity science". Physical Review Special Topics: Physics Education Research. 10 (2): 020122. Bibcode:2014PRPER..10b0122F. doi:10.1103/PhysRevSTPER.10.020122. http://hdl.handle.net/10613/2583. </ref>
  
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Also, the computation law of reachable optimality gives out the boundary between the complexity model, chaotic model, and determination model. When RAYG is the Optimal Choice computation, and the reaching pattern is a persistently positive experience path, persistently negative experience path, or mixed persistent pattern experience path, the underlying computation shall be a simple system computation adopting determination rules. If the reaching pattern has no persistent pattern experienced in the RAYG regime, the underlying computation hints there is a chaotic system. When the optimal choice computation involves non-RAYG computation, it's a complexity computation driving the compound effect.
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=== 复杂性与建模 ===
  
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== Notable scholars ==
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弗里德里希·哈耶克 F. A. Hayek对早期复杂性理论的主要贡献之一，是他对“人类预测简单系统行为的能力”与“透过建模预测复杂系统行为的能力”二者之间的区别。 他认为，经济学和一般复杂现象的科学一样，都包括生物学、心理学等等，不能像物理处理本质上简单现象一样去建模<ref>["Reason Magazine - The Road from Serfdom" "Reason Magazine - The Road from Serfdom"]. Archived from the original on 2007-03-10. Retrieved 2017-09-22.</ref>。哈耶克明确地解释了通过建模的复杂现象，只能对模式进行预测，而不能对非复杂现象进行精确的预测。<ref> [http://nobelprize.org/nobel_prizes/economics/laureates/1974/hayek-lecture.html Friedrich August von Hayek - Prize Lecture]</ref>
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+
 
 +
=== 复杂性与混沌理论 ===
 +
复杂性理论起源于混沌理论，而混沌理论又起源于一个多世纪前法国数学家朱尔斯·亨利·庞加莱 Jules HenriPoincaré的著作。混沌有时被视为极其复杂的信息，而不是无序信息。<ref>Hayles, N. K. (1991). [https://books.google.com/books?hl=en&lr=&id=9g9QDwAAQBAJ&oi=fnd&pg=PR7&dq=%22Chaos+Bound:+Orderly+Disorder+in+Contemporary+Literature+and+science%22&ots=1YiHUgn5wY&sig=sKu7-CerpexzdUT6o-PhVk_Ld9U#v=onepage&q=%22Chaos%20Bound%3A%20Orderly%20Disorder%20in%20Contemporary%20Literature%20and%20science%22&f=false Chaos Bound: Orderly Disorder in Contemporary Literature and Science.] Cornell University Press, Ithaca, NY.</ref>混沌系统扔保持确定性，尽管它们的长期行为很难精确预测。 通过对初始条件和描述混沌系统行为的相关方程等完整的信息，人们可以在理论上对系统做出完美的精确预测，尽管在实践中这是不可能做到任意精确。 伊利亚 · 普里高金 Ilya Prigogine认为<ref>Prigogine, I. (1997). The End of Certainty, The Free Press, New York.</ref> 复杂性是不确定的，无论如何都无法精确地预测未来。<ref>See also D. Carfì (2008). [http://cab.unime.it/journals/index.php/AAPP/article/view/384/0 "Superpositions in Prigogine approach to irreversibility".] AAPP: Physical, Mathematical, and Natural Sciences. 86 (1): 1–13.</ref>
 +
 
 +
复杂性理论中的涌现展示了一个介于确定性秩序和随机性之间复杂的领域<ref name = "34a">Cilliers, P. (1998). Complexity and Postmodernism: Understanding Complex Systems, Routledge, London.</ref>。 这被称为“混乱的边缘” ''edge of chaos''。<ref name="b">Per Bak (1996). How Nature Works: The Science of Self-Organized Criticality, Copernicus, New York, U.S.c</ref>
 +
[[File:A plot of the Lorenz attractor..png|thumb|right|200px|洛伦兹的蝴蝶.]]
 +
 
 +
在分析复杂系统时，对初始条件的敏感性不如在混沌理论中那样重要。正如科兰德 Colander 所说<ref>Colander, D. (2000). The Complexity Vision and the Teaching of Economics, E. Elgar, Northampton, Massachusetts.</ref>，复杂性研究是混沌研究的对立面。 复杂性是指大量极其复杂和动态变化的关系集合如何产生一些简单的行为模式，而确定性混沌意义上的混沌行为，则是一些相对少量非线性相互作用的结果。<ref name="34a" />
 +
 
 +
因此，'''混沌系统'''与复杂系统的主要区别在于二者对历史演化的依赖性。 混乱的系统不像复杂的系统那样依赖于历史数据<ref>Buchanan, M. (2000). Ubiquity : Why catastrophes happen, three river press, New-York.</ref>。 混沌行为将一个处于平衡状态的系统推向混沌状态，换句话说，系统超出了我们传统定义的“有序”。另一方面，复杂系统是指系统从混沌的边缘，即远离平衡状态演化。 它们演变到一个临界状态，这个临界状态是由不可逆和意料之外的事件累积而成的，物理学家默里·盖尔曼称之为“冻结事故的积累”''an accumulation of frozen accidents''<ref>Gell-Mann, M. (1995). What is Complexity? Complexity 1/1, 16-19</ref>。在某种意义上，混沌系统可以被看作是复杂系统的一个子集。 它对历史数据没有依赖性。许多真正的复杂系统，在有限周期内具备鲁棒性。 然而，它们确实具有在保持系统完整性的同时发生根本性质变化的潜力。
 +
 
 +
=== 复杂性与网络科学 ===
 +
 
 +
一个复杂的系统通常由许多组成部分及其相互作用组成。 这样一个系统可以用一个网络来表示，其中节点代表组成部分，连边代表它们之间的相互作用。<ref name="c" /> <ref>Dorogovtsev, S.N.; Mendes, J.F.F. (2003). Evolution of Networks. Adv. Phys. 51. p. 1079. arXiv:cond-mat/0106144. doi:10.1093/acprof:oso/9780198515906.001.0001. ISBN 9780198515906. </ref><ref>Fortunato, Santo (2011). "Reuven Cohen and Shlomo Havlin: Complex Networks". Journal of Statistical Physics. 142 (3): 640–641. Bibcode:2011JSP...142..640F. doi:10.1007/s10955-011-0129-7. ISSN 0022-4715.</ref><ref>Newman, Mark (2010).[http://cds.cern.ch/record/1281254 Networks]. doi:10.1093/acprof:oso/9780199206650.001.0001. ISBN 9780199206650. </ref>例如，因特网可以表示为一个由节点(计算机)和连边(计算机之间的直接连接)组成的网络。 利用渗流理论 percolation theory <ref>Cohen, Reuven; Erez, Keren; ben-Avraham, Daniel; Havlin, Shlomo (2001). "Cohen, Erez, ben-Avraham, and Havlin Reply". Physical Review Letters. 87 (21): 219802. Bibcode:2001PhRvL..87u9802C. doi:10.1103/PhysRevLett.87.219802. ISSN 0031-9007.</ref>研究了其对故障的恢复能力。 其他的例子还有社交网络、航空公司网络<ref>Barrat, A.; Barthelemy, M.; Pastor-Satorras, R.; Vespignani, A. (2004). [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC374315 "The architecture of complex weighted networks". Proceedings of the National Academy of Sciences]. 101 (11): 3747–3752. arXiv:cond-mat/0311416. Bibcode:2004PNAS..101.3747B. doi:10.1073/pnas.0400087101. ISSN 0027-8424. PMC 374315. PMID 15007165</ref>、生物网络和气候网络<ref>Yamasaki, K.; Gozolchiani, A.; Havlin, S. (2008). "Climate Networks around the Globe are Significantly Affected by El Niño". Physical Review Letters. 100 (22): 228501. Bibcode:2008PhRvL.100v8501Y. doi:10.1103/PhysRevLett.100.228501. ISSN 0031-9007. PMID 18643467.</ref>，网络也可能失效也会自动恢复。 为了建立这种现象的模型，可以查看 Majdandzic 等人的研究<ref name="a" />。复杂系统之间的相互作用也可以被建模为网络的网络。 关于它们的故障和恢复特性，见 Gao 等人的研究<ref>Gao, Jianxi; Buldyrev, Sergey V.; Stanley, H. Eugene; Havlin, Shlomo (2011).[http://cps-www.bu.edu/hes/articles/gbsh12.pdf  "Networks formed from interdependent networks" ](PDF). Nature Physics. 8 (1): 40–48. Bibcode:2012NatPh...8...40G. CiteSeerX 10.1.1.379.8214. doi:10.1038/nphys2180. ISSN 1745-2473.</ref> <ref name="9a" />。城市交通可以表示为一个网络，加权链路表示两个节点(节点)之间的速度。 这种方法在衡量一个城市的整体交通效率时是很有用的<ref>Li, Daqing; Fu, Bowen; Wang, Yunpeng; Lu, Guangquan; Berezin, Yehiel; Stanley, H. Eugene; Havlin, Shlomo (2015-01-20). "[https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4311803 Percolation transition in dynamical traffic network with evolving critical bottlenecks]". Proceedings of the National Academy of Sciences. 112 (3): 669–672. Bibcode:2015PNAS..112..669L. doi:10.1073/pnas.1419185112. ISSN 0027-8424. PMC 4311803. PMID 25552558</ref>。 有关交通及其他基础设施<ref>Limiao Zhang, Guanwen Zeng; Daqing Li, Hai-Jun Huang; H Eugene Stanley, Shlomo Havlin (2019). "Scale-free resilience of real traffic jams". Proceedings of the National Academy of Sciences. 116 (18): 8673–8678. arXiv:1804.11047. Bibcode:2019PNAS..116.8673Z. doi:10.1073/pnas.1814982116. PMC 6500150. PMID 30979803</ref>系统韧性 resilience的定义，可以参考这个<ref>Battiston, Stefano; Caldarelli, Guido; May, Robert M.; Roukny, tarik; Stiglitz, Joseph E. (2016-09-06). [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5018742 "The price of complexity in financial networks"]. Proceedings of the National Academy of Sciences. 113 (36): 10031–10036. Bibcode:2016PNAS..11310031B. doi:10.1073/pnas.1521573113. PMC 5018742. PMID 27555583.</ref>。
 +
 
 +
=== 复杂性的一般计算形式 ===
 +
 
 +
有序系统的可达最优性计算形式的建立<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. ISBN 978-1507658246. Chapter 4.</ref>，揭示了在系统完整性的一般限制内，复杂性计算是有序系统的特定和任何经验路径下的“最优选择”和“最优驱动达成模式超时”的复合计算。
 +
 
 +
可达成优选的计算定律有四个关键组成成分，如下所述：
 +
 
 +
1. '''最优可达性 Reachability of Optimality'''：任何预期的最优应该是可达的。对于有序系统的成员，甚至是有序系统本身，不可达的最优性都是没有意义的。
 +
 
 +
2. '''主导性和一致性 Prevailing and Consistency'''：极大化可达性以探索最佳可利用的最优，是有序系统中所有成员的普遍性计算逻辑，并且适应于有序系统。
 +
 
 +
3. '''条件性 Conditionality '''：可达成性和最优之间可以实现的取舍，主要取决于初始投注能力以及投注能力如何随投注行为触发的收益更新路径而发生演变、如何由基本的奖惩规则赋值。准确地说，这是一系列有条件的事件，下一个事件将发生于从经验路径到达现状之时。
 +
 
 +
4. '''稳健性 Robustness'''：可达成最优所能承受的挑战越多，就路径完整性而言就越稳健。
 +
 
 +
可达成优选定律中也有四个计算特征。
 +
 
 +
1. '''最佳选择 Optimal Choice'''：实现最佳选择的计算可以是非常简单、也可以非常复杂。在最佳选择中的一个简单规则，就是接受所达成的任何事情。“按件奖励” Reward As You Go（ RAYG），当 RAYG 被采用时，可达最优计算将减少到最优化的可达性。当达成的游戏中存在多个'''纳什平衡 Nash equilibrium''' 策略时，最优选择计算可能更为复杂。
 +
 
 +
2. '''初始状态 Initial Status'''：计算被假设从一个有兴趣的起点开始，甚至一个有序系统的绝对起点本质上可能不存在，也不需要存在。假设的中性初始状态有利于人工或模拟计算，预计不会改变任何发现的普遍性。
 +
 
 +
3. '''领域 Territory'''：一个有序系统应该有一个域，由系统发起的通用计算，将产生一个仍然在域内的最优解。
 +
 
 +
4. '''达成模式 Reaching Pattern'''：在计算空间中的达成模式、或者在计算空间中的最优驱动达成模式的形式，主要依赖于计算空间下度量空间的性质和维度、以及实现可达的经验路径的惩罚和奖励规则。我们感兴趣的经验路径有五种基本形式：持续正向增强经验路径、持续负向增强经验路径、混合持续型经验路径、衰减规模经验路径和选择经验路径。
 +
 
 +
在选择体验路径的复合计算中，包括当前交互和滞后交互，动态拓扑转换  dynamic topological transformation，并暗示有序系统的体验路径中的不变性和方差特征。
 +
 
 +
 
 +
同时，可达成最优的计算形式给出了复杂性模型、混沌性模型、和确定性模型之间的界限。当 “按件奖励”RAYG是最优选择计算，并且可达模式是持续正向经验路径、持续负向经验路径、或混合持久模式经验路径时，其底层计算应该是采用确定规则的简单系统计算。如果可达模式没有在 RAYG 体制中经历的持续模式，基础计算则提示有混沌系统。当最佳选择计算涉及非 RAYG 计算时，此为复杂性计算所驱动的复合效应。
 +
 
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== 著名学者 ==
 
{{columns-list|colwidth=20em|
 
{{columns-list|colwidth=20em|
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* [[Robert McCormick Adams Jr.|Robert McCormick Adams]]
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*罗伯特·麦考密克·亚当斯 Robert McCormick Adams
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* [[Christopher Alexander]]
+
 
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* [[Philip Warren Anderson|Philip Anderson]]
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*斯图尔特 · 考夫曼 Stuart Kauffma
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* [[Kenneth Arrow]]
+
 
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* [[Robert Axelrod]]
+
*克里斯托弗·亚历山大 Christopher Alexander
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* [[W. Brian Arthur]]
+
 
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* [[Yaneer Bar-Yam]]
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*大卫·克拉考尔 David Krakauer
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* [[Albert-László Barabási|Albert-Laszlo Barabasi]]
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* [[Gregory Bateson]]
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*菲利普·安德森 Philip Anderson
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* [[Ludwig von Bertalanffy]]
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* [[Samuel Bowles (economist)|Samuel Bowles]]
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*埃伦·利维 Ellen Levy
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* [[Guido Caldarelli]]
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* [[Paul Cilliers]]
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*肯尼思·阿诺 Kenneth Arrow
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* [[Walter Clemens, Jr.]]
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* [[James P. Crutchfield]]
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*罗伯特·梅 Robert May
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* [[Brian J. Enquist|Brian Enquist]]
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* [[Joshua M. Epstein|Joshua Epstein]]
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*罗伯特·阿克塞尔罗德 Robert Axelrod
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* [[J. Doyne Farmer|Doyne Farmer]]
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* [[Jay Forrester]]
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*梅拉妮·米歇尔 Melanie Mitchell
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* [[Murray Gell-Mann]]
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* [[Nigel Goldenfeld]]
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*布莱恩·阿瑟 W. Brian Arthur
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* [[James Hartle]]
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* [[John Henry Holland|John Holland]]
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*克里斯·摩尔 Cris Moore
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* [[Alfred Hübler|Alfred Hubler]]
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* [[Arthur Iberall]]
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*杨纳尔·巴亚姆 Yaneer Bar-Yam
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* [[Stuart Kauffman]]
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* [[David Krakauer (scientist)|David Krakauer]]
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*埃德加·莫林 Edgar Morin
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* [[Ellen Levy]]
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* [[Robert May, Baron May of Oxford|Robert May]]
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*阿尔伯特·巴拉巴西 Albert-laszlo Barabasi
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* [[Melanie Mitchell]]
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* [[Cris Moore]]
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*哈罗德·莫罗维茨 Harold Morowitz
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* [[Edgar Morin]]
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* [[Harold J. Morowitz|Harold Morowitz]]
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*格雷戈里 · 贝特森 Gregory Bateson
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* [[Scott_E._Page|Scott Page]]
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* [[Luciano Pietronero]]
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*斯科特·佩奇 Scott Page
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* [[David Pines]]
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* [[Ilya Prigogine]]
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*路德维希·冯·贝塔郎菲 Ludwig von Bertalanffy
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* [[Sidney Redner]]
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* [[Jerry Sabloff]]
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*卢西亚诺·皮埃特罗内罗 Luciano Pietronero
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* [[Cosma Shalizi]]
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* [[Dave Snowden]]
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*杰弗里·韦斯特 Geoffery West
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* [[Sergei Starostin]]
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* [[Steven Strogatz]]
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*史蒂芬·沃尔弗拉姆 Stephen Wolfram
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* [[Alessandro Vespignani]]
+
 
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* [[Andreas Wagner]]
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*邓肯·沃茨 Duncan J Watts
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* [[Duncan J. Watts|Duncan Watts]]
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* [[Geoffrey West]]
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*阿尔弗雷德·布勒 Alfred Hübler
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* [[Stephen Wolfram]]
+
 
−
* [[David Wolpert]]
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*默里·盖尔曼 Murray Gell-Mann
 +
 
 +
*约书亚·爱泼斯坦 Joshua Epstein
 +
 
 +
*约翰·霍兰德 John Holland
 +
 
 +
*杰·韦瑞特·弗瑞斯特 Jay Wright Forrester
 +
 
 +
*戴夫·斯诺登 Dave Snowden
 +
 
 +
*亚历山德罗·韦斯皮尼亚尼 Alessandro Vespignani
 
}}
 
}}
  
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== See also ==
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== 相关概念 ==
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{{Portal|Systems science}}
 
 
{|
 
{|
 
|- style="vertical-align:top"
 
|- style="vertical-align:top"
 
|style="padding-right:2em"|
 
|style="padding-right:2em"|
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* [[Biological organisation]]
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* 生物组织 Biological organisation
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* [[Chaos theory]]
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* [[混沌理论 Chaos theory]]
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* [[Cognitive model#Dynamical systems|Cognitive modeling]]
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* 认知模型 Cognitive model
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* [[Cognitive Science]]
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* 认知科学 Cognitive Science
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* [[Complex (disambiguation)]]
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* [[复杂适应系统 Complex adaptive system]]
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* [[Complex adaptive system]]
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* [[复杂网络 Complex networks]]
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* [[Complex networks]]
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* 复杂性 Complexity
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* [[Complexity]]
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* [[复杂经济学 Complexity economics]]
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* [[Complexity (disambiguation)]]
 
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* [[Complexity economics]]
 
 
|style="padding-right:2em"|
 
|style="padding-right:2em"|
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* [[Cybernetics]]
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* [[控制论 Cybernetics]]
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* [[Decision engineering]]
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* 决策工程 Decision engineering
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* [[Dissipative system]]
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* [[耗散系统 Dissipative system]]
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* [[Dual-phase evolution]]
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* [[双相演化 Dual-phase evolution]]
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* [[Dynamical system]]
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* [[动力系统 Dynamical system]]
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* [[Dynamical systems theory]]
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* [[动态系统理论 Dynamical systems theory]]
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* [[Emergence]]
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* [[涌现 Emergence]]
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* [[Enterprise systems engineering]]
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* 企业系统工程 Enterprise systems engineering
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* [[Fractal]]
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* [[分形 Fractal]]
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* [[Generative sciences]]
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* [[生成科学 Generative science]]
 
|style="padding-right:2em"|
 
|style="padding-right:2em"|
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* [[Hierarchy theory]]
+
* 顺势动力学 Homeokinetics
−
* [[Homeokinetics]]
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* 看不见的手 Invisible hand
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* [[Interdependent networks]]
+
* [[相互依赖网络 Interdependent networks]]
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* [[Invisible hand]]
+
* 混合现实 Mixed reality
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* [[Mixed reality]]
+
* [[多智能系统 Multi-agent system]]
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* [[Multi-agent system]]
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* [[网络科学 Network science]]
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* [[Network science]]
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* [[非线性 Nonlinearity]]
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* [[Nonlinearity]]
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* 模式导向建模 Pattern-oriented modeling
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* [[Pattern-oriented modeling]]
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* 渗流 Percolation
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* [[Percolation]]
+
* 渗流理论 Percolation theory
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* [[Percolation theory]]
 
 
|
 
|
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* [[Process architecture]]
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* 流程架构 Process architecture
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* [[Self-organization]]
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* [[自组织 Self-organization]]
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* [[Sociology and complexity science]]
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* 社会学和复杂系统理论 Sociology and complexity science
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* [[System accident]]
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* 系统性事故 System accident
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* [[System dynamics]]
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* 系统动力学 System dynamics
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* [[System equivalence]]
+
* 系统等效性 System equivalence
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* [[Systems theory]]
+
* [[系统理论 Systems theory]]
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** [[Systems theory in anthropology|in anthropology]]
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** 人类学系统论 System theory in anthropology
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* {{longitem|style=line-height:1.35em|[[Volatility, uncertainty, complexity and ambiguity|Volatility, uncertainty, complexity<br/>and ambiguity]]}}
+
* 波动性、不确定性、复杂性、模糊性（VUCA) Volatility, uncertainty, complexity<br/>and ambiguity
 
|}
 
|}
  
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== References ==
+
== 进一步阅读 ==
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{{Reflist}}
+
* [http://amaral-lab.org/media/publication_pdfs/Amaral-2004-Eur.Phys.J.B-38-147.pdf L.A.N. Amaral and J.M. Ottino, Complex networks — augmenting the framework for the study of complex system, 2004]
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+
* Chu, D.; Strand, R.; Fjelland, R. (2003). "Theories of complexity". Complexity. 8 (3): 19–30. Bibcode:2003Cmplx...8c..19C. doi:10.1002/cplx.10059.
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== Further reading ==
+
* Walter Clemens, Jr., [https://web.archive.org/web/20150219221633/http://www.sunypress.edu/p-5782-complexity-science-and-world-af.aspx Complexity Science and World Affairs], SUNY Press, 2013.
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* [https://complexityexplained.github.io Complexity Explained].
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* Gell-Mann, Murray (1995). "[http://www.santafe.edu/~mgm/Site/Publications_files/MGM%20118.pdf Let's Call It Plectics"] (PDF). Complexity. 1 (5): 3–5. Bibcode:1996Cmplx...1e...3G. doi:10.1002/cplx.6130010502.[permanent dead link]
−
* [[Luis Amaral|L.A.N. Amaral]] and J.M. Ottino, [http://amaral-lab.org/media/publication_pdfs/Amaral-2004-Eur.Phys.J.B-38-147.pdf ''Complex networks — augmenting the framework for the study of complex system''], 2004.
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* A. Gogolin, A. Nersesyan and A. Tsvelik, [https://web.archive.org/web/20070715195144/http://www.cmth.bnl.gov/~tsvelik/theory.html Theory of strongly correlated systems], Cambridge University Press, 1999.
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* {{cite journal | last1 = Chu | first1 = D. | last2 = Strand | first2 = R. | last3 = Fjelland | first3 = R. | year = 2003 | title = Theories of complexity | url = | journal = Complexity | volume = 8 | issue = 3 | pages = 19–30 | doi = 10.1002/cplx.10059 | bibcode = 2003Cmplx...8c..19C }}
+
* Nigel Goldenfeld and Leo P. Kadanoff, [http://guava.physics.uiuc.edu/~nigel/articles/complexity.html Simple Lessons from Complexity], 1999
−
* [[Walter Clemens, Jr.]], [https://web.archive.org/web/20150219221633/http://www.sunypress.edu/p-5782-complexity-science-and-world-af.aspx ''Complexity Science and World Affairs''], SUNY Press, 2013.
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* Kelly, K. (1995). Out of Control, Perseus Books Group.
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* {{cite journal | last1 = Gell-Mann | first1 = Murray | year = 1995 | title = Let's Call It Plectics | url = http://www.santafe.edu/~mgm/Site/Publications_files/MGM%20118.pdf | journal = Complexity | volume = 1 | issue = 5 | doi = 10.1002/cplx.6130010502 | pages = 3–5 | bibcode = 1996Cmplx...1e...3G }}{{Dead link|date=August 2019 |bot=InternetArchiveBot |fix-attempted=yes }}
+
* Syed M. Mehmud (2011), [https://web.archive.org/web/20120426052819/http://predictivemodeler.com/sitecontent/book/Ch06_Applications/Actuarial/HEC_Model/Healthcare%20Exchange%20Complexity%20Model%20-%20Report%20-%20Aug2011.pdf A Healthcare Exchange Complexity Model]
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* A. Gogolin, A. Nersesyan and A. Tsvelik, [https://web.archive.org/web/20070715195144/http://www.cmth.bnl.gov/~tsvelik/theory.html ''Theory of strongly correlated systems ''], Cambridge University Press, 1999.
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* Preiser-Kapeller, Johannes,[Preiser-Kapeller, Johannes, "Calculating Byzantium. Social Network Analysis and Complexity Sciences as tools for the exploration of medieval social dynamics". August 2010 "Calculating Byzantium. Social Network Analysis and Complexity Sciences as tools for the exploration of medieval social dynamics"]. August 2010
−
* [[Nigel Goldenfeld]] and Leo P. Kadanoff, [http://guava.physics.uiuc.edu/~nigel/articles/complexity.html ''Simple Lessons from Complexity''], 1999
+
* Donald Snooks, Graeme (2008). "[https://www.cbe.anu.edu.au/researchpapers/cepr/DP563.pdf A general theory of complex living systems: Exploring the demand side of dynamics" ](PDF). Complexity. 13 (6): 12–20. Bibcode:2008Cmplx..13f..12S. doi:10.1002/cplx.20225.
−
* Kelly, K. (1995). [http://www.kk.org/outofcontrol/contents.php ''Out of Control''], Perseus Books Group.
+
* Stefan Thurner, Peter Klimek, Rudolf Hanel: Introduction to the Theory of Complex Systems, Oxford University Press, 2018, ISBN 978-0198821939
−
* Syed M. Mehmud (2011), [https://web.archive.org/web/20120426052819/http://predictivemodeler.com/sitecontent/book/Ch06_Applications/Actuarial/HEC_Model/Healthcare%20Exchange%20Complexity%20Model%20-%20Report%20-%20Aug2011.pdf ''A Healthcare Exchange Complexity Model'']
+
* [https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/publication/2016/10/31/Bulletin_Fall_2014_FINAL.pdf SFI @30, Foundations & Frontiers (2014).]
−
* [https://web.archive.org/web/20110220054920/http://www.oeaw.ac.at/byzanz/repository/Preiser_WorkingPapers_Calculating_I.pdf Preiser-Kapeller, Johannes, "Calculating Byzantium. Social Network Analysis and Complexity Sciences as tools for the exploration of medieval social dynamics". August 2010]
 
−
* {{cite journal | last1 = Donald Snooks | first1 = Graeme | year = 2008 | title = A general theory of complex living systems: Exploring the demand side of dynamics | url = https://www.cbe.anu.edu.au/researchpapers/cepr/DP563.pdf| journal = Complexity | volume = 13 | issue = 6 | doi=10.1002/cplx.20225 | pages=12–20| bibcode = 2008Cmplx..13f..12S }}
 
−
* [[Stefan Thurner]], Peter Klimek, Rudolf Hanel: ''Introduction to the Theory of Complex Systems'', Oxford University Press, 2018, {{ISBN|978-0198821939}}
 
−
* [https://sfi-edu.s3.amazonaws.com/sfi-edu/production/uploads/publication/2016/10/31/Bulletin_Fall_2014_FINAL.pdf SFI @30, Foundations & Frontiers] (2014).
 
  
−
== External links ==
+
== 外部链接 ==
−
{{Commons category|Complex systems}}
+
* [http://www.openabm.org/ "The Open Agent-Based Modeling Consortium".]
−
{{Wiktionary|complex systems}}
+
* [http://www.complexity.ecs.soton.ac.uk/ "Complexity Science Focus".]
−
* {{cite web|url=http://www.openabm.org |title=The Open Agent-Based Modeling Consortium}}
+
* [[圣塔菲研究所 Santa Fe Institute]]
−
* {{cite web|url=http://www.complexity.ecs.soton.ac.uk/ |title=Complexity Science Focus}}
+
* [http://www.lsa.umich.edu/cscs/ "The Center for the Study of Complex Systems, Univ. of Michigan Ann Arbor".]
−
* {{cite web|url=http://www.santafe.edu/ |title=Santa Fe Institute}}
+
* [http://indecs.eu/ "INDECS". (Interdisciplinary Description of Complex Systems)]
−
* {{cite web|url=http://www.lsa.umich.edu/cscs/ |title=The Center for the Study of Complex Systems, Univ. of Michigan Ann Arbor}}
+
* [http://www.complexityexplorer.org/courses/89-introduction-to-complexity "Introduction to Complexity - Free online course by Melanie Mitchell" "Introduction to Complexity - Free online course by Melanie Mitchell".]
−
* {{cite web|url=http://indecs.eu/ |title=INDECS}} (Interdisciplinary Description of Complex Systems)
+
* Jessie Henshaw (October 24, 2013).[http://www.eoearth.org/view/article/51cbed507896bb431f69154d/?topic=51cbfc79f702fc2ba8129ed7 "Complex Systems"]. Encyclopedia of Earth.
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* {{cite web|url=http://www.complexityexplorer.org/courses/89-introduction-to-complexity |title=Introduction to Complexity - Free online course by Melanie Mitchell}}
+
* [http://havlin.biu.ac.il/course1.php Introduction to complex systems-short course by Shlomo Havlin]
−
* {{cite web|url=http://www.eoearth.org/view/article/51cbed507896bb431f69154d/?topic=51cbfc79f702fc2ba8129ed7 |title=Complex Systems|date=October 24, 2013|author=Jessie Henshaw|publisher=[[Encyclopedia of Earth]]}}
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* [http://www.scholarpedia.org/article/Complex_Systems Complex systems]in scholarpedia.
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* [https://web.archive.org/web/20151114085247/http://havlin.biu.ac.il/course1.php Introduction to complex systems-short course by Shlomo Havlin]
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* [http://cssociety.org/ Complex Systems Society]
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* [http://www.scholarpedia.org/article/Complex_Systems Complex systems] in scholarpedia.
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* [https://en.wikipedia.org/wiki/Complexity_Science_Hub_Vienna Complexity Science Hub Vienna]
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* [http://cssociety.org Complex Systems Society]
 
−
*[[Complexity Science Hub Vienna]]
 
 
* [https://web.archive.org/web/20080723135438/http://www.complexsystems.net.au/ (Australian) Complex systems research network.]
 
* [https://web.archive.org/web/20080723135438/http://www.complexsystems.net.au/ (Australian) Complex systems research network.]
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* [https://web.archive.org/web/20091130204009/http://informatics.indiana.edu/rocha/complex/csm.html Complex Systems Modeling] based on [[Luis M. Rocha]], 1999.
+
* [https://web.archive.org/web/20091130204009/http://informatics.indiana.edu/rocha/complex/csm.html Complex Systems Modeling] based on Luis M. Rocha, 1999.
 
* [https://web.archive.org/web/20110722075059/http://www.crm.cat/ComplexSystems_Lines/defaultsistemescomplexos.htm CRM Complex systems research group]
 
* [https://web.archive.org/web/20110722075059/http://www.crm.cat/ComplexSystems_Lines/defaultsistemescomplexos.htm CRM Complex systems research group]
 
* [https://web.archive.org/web/20110430200327/http://www.ccsr.uiuc.edu/ The Center for Complex Systems Research, Univ. of Illinois at Urbana-Champaign]
 
* [https://web.archive.org/web/20110430200327/http://www.ccsr.uiuc.edu/ The Center for Complex Systems Research, Univ. of Illinois at Urbana-Champaign]
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* [http://www.futurict.eu FuturICT — Exploring and Managing our Future]
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* [http://www.futurict.eu/  FuturICT — Exploring and Managing our Future]
 +
 
 +
== 参考文献 ==
 +
<references/>
 +
 
 +
== 编者推荐 ==
 +
推荐一下国内网站上就能访问到的学习资源：
 +
[[File:Complex book.png|200px|缩略图|右|[https://epubw.com/136554.html?__cf_chl_jschl_tk__=650fa1f6baec6e50bd212cca34a24d6536e588ed-1586572229-0-AWh5KH2lhg37JsaaKuovP5CZnyCzY7eCY6aeW_fRTs4XSjMEOnp3YVFAtgqiCcvPTF-HNQKnrGKcwNvN-yZ46HBEPEsZXKsjYMbcQWfnN-jo7UeC3eo57BdcuxTTmjFHiKNxPxoXlrtHDzGqi9WvqbI-gVVkrInLbQrwEXAWnO9-rdJX_iQ15PCNpzBGK7M2KmxWGecYEASZr9AQG5IqiyzPh80zB0fo-sfOL3HOf7ZVbuSVbGCnpDZQ1H7tT7623TaNkBkA1HdwuEvb003WVdlni8aoft8V3qvJIKFGs4DA 电子书《复杂》下载 by <美>梅拉妮•米歇尔（Melanie Mitchell）]]]
 +
 
 +
* [https://pattern.swarma.org/paper?id=dbc0724e-3031-11ea-b484-0242ac1a0005 An Introduction to Complex Systems Science and its Applications]
 +
:: 美国[[新英格兰复杂系统研究所]]（New England Complex Systems Institute, NECSI）的 [[Yaneer Bar-Yam]]（创始人及所长）和 Alexander F. Siegenfeld 近期写的一篇综述，梳理了复杂性研究的共识，全面介绍了复杂系统科学这一领域的基本原理、常用方法和应用方向。集智俱乐部对此进行了翻译整理。[https://swarma.org/?p=18060 新英格兰复杂系统研究所长文综述：复杂系统科学及其应用]
 +
 
 +
* 北京师范大学系统科学学院狄增如教授梳理了[https://campus.swarma.org/play/coursedetail?id=10665 系统科学的基础概念]。
 +
 
 +
* 北京师范大学系统科学学院[https://campus.swarma.org/play/coursedetail?id=394 陈清华副教授对幂律分布基础知识]的分享。
 +
 
 +
* 北京师范大学系统科学学院[https://campus.swarma.org/play/coursedetail?id=420 2019夏令营视频]记录。
 +
 
 +
* 北京师范大学、集智俱乐部创始人张江教授关于入门复杂系统的思维性课程，一套新的价值观：[https://campus.swarma.org/play/coursedetail?id=10665 复杂性思维]
 +
 
 +
* 北京师范大学系统科学学院吴金闪老师出的[https://sss.bnu.edu.cn/~jinshanw/doc/InvitationtoSS.pdf 系统科学基础]的电子书，配套的学习视频。
 +
::[https://campus.swarma.org/play/coursedetail?id=137 系统科学导引（一）：概论部分]
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::[https://campus.swarma.org/play/coursedetail?id=138 系统科学导引（二）：数学部分]
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::[https://campus.swarma.org/play/coursedetail?id=139 系统科学导引（三）：物理部分]
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::[https://campus.swarma.org/play/coursedetail?id=140 系统科学导引（四）：量子力学]
 +
 
 +
* '''复杂系统科普入门'''： 复杂 Complexity 梅拉妮·米歇尔 Melanie Mitchell
 +
::梅拉妮是道格拉斯·侯世达 Douglas Hofstadter的学生，目前在波特兰大学执教。主要工作方向是类比推理、复杂系统、基因算法与元胞自动机。《复杂》自2009出版后，一路好评，豆瓣评分9分。从起源、演进、定义、度量几个方面介绍什么是复杂系统。
 +
 
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 +
----
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本中文词条由[[用户:思无涯咿呀咿呀|思无涯咿呀咿呀]]参与编译，[[用户:苏格兰|苏格兰]]审校，[[用户:薄荷|薄荷]]、[[用户:费米子|费米子]]编辑，欢迎在讨论页面留言。
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'''本词条内容源自wikipedia及公开资料，遵守 CC3.0协议。'''
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2020年7月15日 (三) 10:32的版本


复杂系统 complex system由许多相互作用的元素组成。复杂系统的例子无处不在：全球气候、有机体、人脑、电网、交通、通讯系统等基础设施网络、城市社会和经济组织网络、生态系统、活细胞、甚至整个宇宙，这些都可以看作是复杂系统。

复杂系统是指那些本身难以直接建模的系统，因为系统组成元素之间以及系统和环境之间存在依赖、竞争、关联等复杂的相互作用。系统之所以“复杂”，是因为在这些相互作用中会产生如非线性 nonlinearity、涌现 emergence、自发秩序 spontaneous order 、适应性 adaptation以及反馈回路 feedback loops等特殊性质。因为这些系统出现在不同领域，所以对不同领域系统的共性研究慢慢发展成为一个独立的研究领域。大部分情况下，复杂系统都可以表示成一个网络，网络中的节点表示元素，连边表示相互作用。

复杂系统理论是系统科学中的一个前沿方向，它是复杂性科学的主要研究任务。复杂性科学被称为21 世纪的科学，它的主要目的就是要揭示复杂系统的一些难以用现有科学方法解释的动力学行为。与传统的还原论方法不同，复杂系统理论强调用整体论和还原论相结合的方法去分析系统。目前，复杂系统理论还处于萌芽阶段，它可能蕴育着一场新的系统学乃至整个传统科学方法的革命。生命系统、社会系统都是复杂系统，复杂系统理论的应用在系统生物学的研究与生物系统计算机数学建模中具有重要的意义。

复杂系统涵盖的主题

概览

复杂系统这一术语，通常是指对复杂系统的研究，表示一种新的科学研究方法。主要研究：系统元素之间的关系如何产生集体行为，系统和环境之间如何进行相互作用，将集体、系统层面的行为作为研究的基本对象[1]。因此，复杂系统可以看作是还原论 reductionism的替代范式，主要解释系统的组成部分和相互关系。

作为一个跨学科的研究领域，复杂系统吸收了许多其他领域的研究理论，如借鉴物理学对自组织 self-organization的研究，社会科学对自发秩序 spontaneous order的研究，数学对混沌 chaos的研究，生物学对适应性 adaptation的研究。因此“复杂系统”是一个宽泛的术语，涵盖了不同领域的研究方法，包括统计物理学、信息论、非线性动力学、人类学、计算机科学、气象学、社会学、经济学、心理学和生物学等。

复杂系统的共性

  • 个人一般都遵循相对简单的规则，不存在中央控制或者领导者。
  • 大量个体的集体行为产生出了复杂、不断变化而且难以预测的行为模式。
  • 利用来自内部和外部环境中的信息和信号，同时也产生信息和信号。
  • 可以通过学习和进化过程进行适应，即改变自身的行为以增加生存或成功的机会。

总结：复杂系统由大量组分组成的网络：不存在中央控制；通过简单运作规则产生出复杂的集体行为和复杂的信息处理，并通过学习和进化产生适应性。

重要概念

系统

开放系统的输入和输出流，代表系统和周围环境之间的问题、能量和信息之间的交换

复杂系统主要关注的是系统的行为和性质。一个系统 system，广义地讲，是由一组实体，通过实体之间的交互、关联、或者依赖，形成一个统一的整体。系统一般由边界来定义，边界决定了哪些属于系统内的一部分，而位于系统边界之外的部分则构成了该系统的环境。一个系统可以表现出与系统个体行为和性质不一样的特性。这些系统层面（整体）的性质和特征通过系统与环境相互作用，或者由系统的部分行为体现出来（例如，对外部刺激作出反应）。此处“行为”的概念意味着，研究系统也涉及到对随时间演化的过程研究（或者，在数学中，叫做相空间参数化）。 由于其广泛的、跨学科的适用性，系统是复杂系统中极其重要的概念。


作为一个研究领域，复杂系统是系统论的一个子领域。 尽管广义的系统理论也侧重于研究相互作用实体的集体行为，但复杂系统研究的是更广泛的一类系统，包括传统还原论方法也能适用的非复杂系统。事实上，系统理论试图探索和描述所有类型的系统，主要目标就是发明对各研究领域都有用的理论。

至于系统理论和复杂系统的关系，系统理论强调系统各部分之间的关系和依赖在一定程度上决定了整个系统的性质，有助于说明复杂系统的跨学科研究视角：具有共享属性的概念连接了不同领域的系统，同时证明无论是什么样的复杂系统，都可以通过建模方法对系统进行科学研究。同时复杂系统重要的特定概念，如涌现 emergence、反馈回路 feedback loops和适应性 adaptation，也起源于系统理论。

复杂性

“系统表现出复杂性”意味着很难从其行为中推断出系统的性质。任何忽略这些差异和特性，或者将差异和特性视为噪声的建模方法都是不准确也没有效果的。到目前为止，还没有完全通用的复杂系统理论来解决这些问题，因此研究人员必须结合特定的领域解决问题。研究人员解决这些问题的方法是将建模的主要任务看做是刻画复杂性，而不简化系统的复杂性。

虽然目前还没有被广泛认可的复杂性的精确定义，但是有很多关于复杂性的典型例子。例如，如果系统具有混沌行为(对初始条件表现出极度敏感的行为) ，或者如果它们具有涌现特性(这些特性从它们的组成元素中看不出来，但来源于在一个系统中产生的关系和依赖) ，或者如果它们难以计算建模(如果它们的参数数量的增加快于系统大小的增加) ，那么系统就可能是复杂的。

网络

复杂系统中相互作用的部分组成一个网络，网络是离散对象及其相互关系的集合，通常描述为由边连接的顶点图。 网络可以描述系统中个体之间的关系，例如：电路中逻辑门之间的关系，基因调控网络中的基因之间的关系，或者任何其他相关实体之间的关系。

网络经常用来刻画复杂系统中的复杂性。因此，把复杂系统当作网络来研究，可以使图论和网络科学 network science得到广泛应用。例如，一些复杂系统也是复杂网络，它们具有相变和幂律度分布等特性，这些特性容易导致涌现或混沌行为。一个完全图中，边的数量随着顶点数量的增加而幂次增长，这一特性进一步揭示了大型网络中复杂性的来源: 随着网络的增长，实体之间的关系增加要远快于实体数量的增加。

非线性

洛伦兹吸引子当 ρ = 28, σ = 10, and β = 8/3 [2]

复杂系统通常具有非线性行为，意味着输入相同的状态和内容，系统可能会作出不同的回应。在数学和物理学中，非线性描述的是输入和输出不成比例的系统。当给定输入变化时，系统产生的结果可能远大于或远小于输入的变化，甚至根本没有输出（这取决于系统当前的状态或参数值的取值）。

复杂系统中一个有意思的研究就是非线性动力系统，它是由一个或多个非线性项组成的微分方程组。一些非线性动力系统，如洛伦兹系统，可以产生一种称为混沌的数学现象。 混沌，适用于复杂系统，通常是指是指对初始条件的敏感依赖，如“蝴蝶效应” 。在这样一个系统中，小的初始改变状态可能会导致截然不同的结果。因此，混沌行为的数值模拟非常困难，因为在计算的中间阶段，很小的扰动误差会导致模型产生极为不准确的结果。此外，即使在想他刺激下，如果一个复杂的系统回到一个之前的初始状态，它可能会表现出和之前状态完全不一样的行为，完全不同的行为反应，所以混沌也对经验推断的方式提出了挑战。

涌现

复杂系统的另一个共同特征是涌现行为和特性的存在：这些是系统层面的特征，无法从其组成部分中孤立地表现出来，而是由它们在系统中一起形成的相互作用、依赖或关系所形成。涌现广泛地描述了这类行为的出现，并且在社会科学和物理科学研究的系统中都有广泛应用。涌现通常是指复杂系统中出现的无计划却有组织的行为，也可以指系统的崩溃，可用于描述从组成系统的较小实体层面难以预测或无法预测的现象。

康威生命游戏中出现的枪型的元胞自动机

在复杂系统中，涌现特性被广泛研究的其中一个例子就是元胞自动机 Cellular Automata。在元胞自动机中，一个由细胞组成的网格，每个细胞都是处于某种状态，且这些状态是有限的，然后根据一组简单的规则进行演化。这些规则指导每个细胞与其邻近细胞进行“相互作用”。 尽管这些规则只是局部定义的，但是它们已经被证明能够产生全局性的有趣行为，例如康威的生命游戏 Conway's Game of Life。

自发秩序与自组织

当涌现用于描述无计划的秩序出现时，是指自发秩序(在社会科学中)或自组织(在物理科学中)。自发秩序可以在羊群行为中看到，即一群个体在没有集中计划安排的情况下协调他们的行动；在某些晶体的整体对称性中可以看到自组织，例如雪花的径向对称性，这种对称性来自于水分子与其周围环境之间的局部吸引力和排斥力。

适应

复杂适应系统 Complex Adaptive Systems，简称CAS，是复杂系统的特例，这类系统具有改变和从经验中学习的能力，因此具有适应性。复杂适应系统的例子包括股票市场，社会昆虫，蚁群、生物圈和生态系统，大脑和免疫系统、细胞和发育中的胚胎，城市、制造业和在文化和社会系统中比如政党或者社区等人类社会群体活动。 [3]

功能

复杂系统可能具有以下特征[4]：

级联失效

由于复杂系统中组成部分之间的强耦合性，一个或多个组成部分的失效可能导致级联失效，这可能对系统的运行造成灾难性的后果[5]。局部攻击可能导致空间网络的级联失效或突然崩溃。[6]

开放系统

复杂系统通常是开放系统，即存在热力学梯度和耗散能量。换句话说，复杂系统经常远离能量平衡态: 但是尽管存在这种变动，仍然可能存在稳定的模式，参见协同作用 synergetics。

系统演化

一个系统的演化过程可能是非常重要的，因为复杂系统是随着时间演化的动力系统，历史状态可能对当前状态有影响。 更正式地说，复杂系统往往表现出自发故障 spontaneous failures、恢复 recovery 以及磁滞 hysteresis。[7]。 当延迟的负反馈导致振荡或其他复杂动力学变弱时[8]，系统状态空间中的“临界减速方向”可能预示着系统在这种“临界转换”之后的未来状态。相互作用系统可能具有许多相变的复杂滞后现象。[9]

系统嵌套

复杂系统的组成部分也可能是一个复杂系统。 例如，一个经济体是由组织构成的，这些组织是由人构成的，这些人是由细胞构成的——而所有这些（经济体、组织、人、细胞）都可以看作是复杂系统。 在复杂的二分网络中，相互作用的排列也可以是嵌套的。 更具体地说，互相进行有益交互的二分生态和组织网络被发现具有嵌套结构。[10] [11] 这种结构提高了间接促进作用和系统在日益严峻的环境下持续存在的能力，以及大规模系统性政权转移的可能性。[12] [13]

网络动力学多样性

除了有耦合规则，复杂系统的网络动力学也是非常重要的。局部相互作用以及少数优先连接在小世界网络或无标度网络[14][15][16]经常被应用，特别是自然复杂系统经常表现出这样的拓扑结构。 例如，在人类的大脑皮层，我们可以看到密集的局部连接，以及一些非常长的轴突在大脑皮层内部和其他大脑区域之间的投射。

涌现现象的产生

复杂系统很多行为都是涌现的。也就是说，虽然结果可能由系统的基本组成部分的活动决定的，但它们需要从更高的层次进行研究分析。 例如，在蚁丘中的白蚁具有生理学特征、生物化学特征和生物学的发育特征，这些都处于一个分析层面的，但是它们的社会行为和蚁丘的建造是白蚁集体层面涌现出来的属性，需要在不同的层面上进行分析。

非线性关系

实际上，这意味着一个小的扰动可能会引发大的效应(见蝴蝶效应 butterfly effect) 或者一个成比例的效应或者甚至根本没有效应。 在线性系统中，效应总是与输入成比例。 而非线性 nonlinearity则相反。

反馈循环

在复杂系统中，经常会存在负反馈和正反馈。 元素行为的影响以元素本身被改变的方式反馈到系统中。

历史

复杂性科学发展地图[17]

可以说，人类研究复杂系统已有数千年的历史，但与物理和化学等已确立的科学领域相比，复杂系统的现代科学研究还相对年轻。 系统科学的研究历史和几种不同的研究趋势有关。

在数学领域，可以说对复杂系统研究的最大贡献是发现了确定性系统中混沌 chaos现象，在某些特定的动力系统有一个重要的特征也与数学有关，即非线性 nonlinearity。[18]神经网络研究的数学部分在推进复杂系统的研究中也是不可或缺的。

自组织系统的概念与非平衡热力学中的研究有关，化学先驱和诺贝尔奖获得者伊利亚 · 普里高金 Ilya Prigogine在他的耗散结构 dissipative structures研究中首次提到这个概念。 更久远的可以追溯到 Hartree-Fock关于量子化学方程的工作，以及后来对分子结构的计算，这些可以被看作是科学上涌现和整体涌现最早的例子之一。

苏格兰启蒙运动的古典政治经济学是一个考虑人类在内的复杂系统，后来由奥地利经济学派发展，其认为市场系统的秩序是自发的(或涌现的) ，因为它是人类行为的结果，而不是任何人类设计的执行。[19][20]

在此基础上，奥地利学派从19世纪到20世纪发展了早期的经济计算 economic calculation problem问题，随后提出了分散知识 dispersed knowledge的概念（即没有一个单一的行为主体拥有影响整个系统的价格和生产的所有因素的信息），这一概念引发了对当时占主导地位的凯恩斯主义的争论。 这场争论引起了经济学家、政治家和其他政党对计算复杂性问题的关注。

诺贝尔经济学奖得主、哲学家弗里德里希·哈耶克 F. A. Hayek是这一领域的先驱，受到卡尔•波普尔 Karl Popper和沃伦•韦弗 Warren Weaver 著作的启发，从20世纪早期到晚期，他的大部分工作致力于研究复杂现象[21]，但他不是将他的工作局限于人类经济，而是涉足心理学[22]、生物学和控制论等其他领域。

此外格雷戈里 · 贝特森 Gregory Bateson在建立人类学和系统论之间的联系方面发挥了关键作用：他指出文化的互动部分很像生态系统。

虽然对复杂系统的明确研究至少可以追溯到20世纪70年代[23]，但第一个专注于复杂系统的研究机构是圣塔菲研究所 Santa Fe Institute，成立于1984年[24][25]。 圣菲研究所的早期参与者包括诺贝尔物理学奖得主默里·盖尔曼 Murray Gell-Mann和 菲利普·安德森 Philip Anderson，诺贝尔经济学奖得主 肯尼思·阿诺 Kenneth Arrow，以及曼哈顿计划的科学家乔治·考温 George Cowan 和 赫伯·安德森 Herb Anderson[26]。到现在已经有50多个专注于复杂系统研究所和研究中心。

应用

实践中的复杂性

传统的处理复杂性的方法是减少或限制的方式。通常情况下，这涉及到部门化 compartmentalization: 将一个大的系统划分成独立的部分。 例如，组织将他们的工作分成不同的部门，每个部门处理不同的问题。 工程系统设计通常采用模块化组件。 然而，当部门之间的连接出现问题时，模块化设计很容易失败。

复杂性管理

随着项目和收购变得越来越复杂，公司和政府面临着挑战去找到有效方法来管理大型收购，例如：陆军未来战斗系统（FCS）。FCS收购依赖于相互关联的部分，而它们之间的相互作用是无法预测的，随着收购变得越来越以网络为中心和复杂化，企业将被迫设法管理复杂性，而政府将面临挑战去提供有效治理，以确保灵活性和韧性 resiliency。[27]

复杂经济学

在过去的几十年里，在复杂经济学 complexity ecomomics的新兴领域中，新的预测模型已经被开发出来，用于解释经济增长。比如1989年由圣菲研究所建立的模型（人工股票市场模型），以及最近由麻省理工学院物理学家塞萨尔·伊达尔戈 César A. Hidalgo和哈佛大学经济学家 里卡多 · 豪斯曼 Ricardo Hausmann 提出的经济复杂性指数 economic complexity index 。基于ECI指数 Economic Complexity Index，Hausmann、Hidalgo 和他们的经济复杂性观测站团队已经做出了2020年的 GDP 预测。

复杂性与教育

福斯曼 Forsman、莫尔 Moll 和林德 Linder关注学生持续学习的问题，探讨了“将复杂性科学作为一个框架来扩展物理教育研究 physics education research法应用的可行性” ，发现“在复杂性科学的视角内构建社会网络分析，为广泛的物理教育研究PER主题提供了新的强大的适用性”。 [28]

复杂性与建模

弗里德里希·哈耶克 F. A. Hayek对早期复杂性理论的主要贡献之一，是他对“人类预测简单系统行为的能力”与“透过建模预测复杂系统行为的能力”二者之间的区别。 他认为，经济学和一般复杂现象的科学一样，都包括生物学、心理学等等，不能像物理处理本质上简单现象一样去建模[29]。哈耶克明确地解释了通过建模的复杂现象，只能对模式进行预测，而不能对非复杂现象进行精确的预测。[30]

复杂性与混沌理论

复杂性理论起源于混沌理论，而混沌理论又起源于一个多世纪前法国数学家朱尔斯·亨利·庞加莱 Jules HenriPoincaré的著作。混沌有时被视为极其复杂的信息，而不是无序信息。[31]混沌系统扔保持确定性，尽管它们的长期行为很难精确预测。 通过对初始条件和描述混沌系统行为的相关方程等完整的信息，人们可以在理论上对系统做出完美的精确预测，尽管在实践中这是不可能做到任意精确。 伊利亚 · 普里高金 Ilya Prigogine认为[32] 复杂性是不确定的，无论如何都无法精确地预测未来。[33]

复杂性理论中的涌现展示了一个介于确定性秩序和随机性之间复杂的领域[34]。 这被称为“混乱的边缘” edge of chaos。[35]

洛伦兹的蝴蝶.

在分析复杂系统时，对初始条件的敏感性不如在混沌理论中那样重要。正如科兰德 Colander 所说[36]，复杂性研究是混沌研究的对立面。 复杂性是指大量极其复杂和动态变化的关系集合如何产生一些简单的行为模式，而确定性混沌意义上的混沌行为，则是一些相对少量非线性相互作用的结果。[34]

因此，混沌系统与复杂系统的主要区别在于二者对历史演化的依赖性。 混乱的系统不像复杂的系统那样依赖于历史数据[37]。 混沌行为将一个处于平衡状态的系统推向混沌状态，换句话说，系统超出了我们传统定义的“有序”。另一方面，复杂系统是指系统从混沌的边缘，即远离平衡状态演化。 它们演变到一个临界状态，这个临界状态是由不可逆和意料之外的事件累积而成的，物理学家默里·盖尔曼称之为“冻结事故的积累”an accumulation of frozen accidents[38]。在某种意义上，混沌系统可以被看作是复杂系统的一个子集。 它对历史数据没有依赖性。许多真正的复杂系统，在有限周期内具备鲁棒性。 然而，它们确实具有在保持系统完整性的同时发生根本性质变化的潜力。

复杂性与网络科学

一个复杂的系统通常由许多组成部分及其相互作用组成。 这样一个系统可以用一个网络来表示，其中节点代表组成部分，连边代表它们之间的相互作用。[16] [39][40][41]例如，因特网可以表示为一个由节点(计算机)和连边(计算机之间的直接连接)组成的网络。 利用渗流理论 percolation theory [42]研究了其对故障的恢复能力。 其他的例子还有社交网络、航空公司网络[43]、生物网络和气候网络[44]，网络也可能失效也会自动恢复。 为了建立这种现象的模型，可以查看 Majdandzic 等人的研究[7]。复杂系统之间的相互作用也可以被建模为网络的网络。 关于它们的故障和恢复特性，见 Gao 等人的研究[45] [9]。城市交通可以表示为一个网络，加权链路表示两个节点(节点)之间的速度。 这种方法在衡量一个城市的整体交通效率时是很有用的[46]。 有关交通及其他基础设施[47]系统韧性 resilience的定义，可以参考这个[48]。

复杂性的一般计算形式

有序系统的可达最优性计算形式的建立[49]，揭示了在系统完整性的一般限制内，复杂性计算是有序系统的特定和任何经验路径下的“最优选择”和“最优驱动达成模式超时”的复合计算。

可达成优选的计算定律有四个关键组成成分，如下所述：

1. 最优可达性 Reachability of Optimality：任何预期的最优应该是可达的。对于有序系统的成员，甚至是有序系统本身，不可达的最优性都是没有意义的。

2. 主导性和一致性 Prevailing and Consistency：极大化可达性以探索最佳可利用的最优，是有序系统中所有成员的普遍性计算逻辑，并且适应于有序系统。

3. 条件性 Conditionality ：可达成性和最优之间可以实现的取舍，主要取决于初始投注能力以及投注能力如何随投注行为触发的收益更新路径而发生演变、如何由基本的奖惩规则赋值。准确地说，这是一系列有条件的事件，下一个事件将发生于从经验路径到达现状之时。

4. 稳健性 Robustness：可达成最优所能承受的挑战越多，就路径完整性而言就越稳健。

可达成优选定律中也有四个计算特征。

1. 最佳选择 Optimal Choice：实现最佳选择的计算可以是非常简单、也可以非常复杂。在最佳选择中的一个简单规则，就是接受所达成的任何事情。“按件奖励” Reward As You Go（ RAYG），当 RAYG 被采用时，可达最优计算将减少到最优化的可达性。当达成的游戏中存在多个纳什平衡 Nash equilibrium 策略时，最优选择计算可能更为复杂。

2. 初始状态 Initial Status：计算被假设从一个有兴趣的起点开始，甚至一个有序系统的绝对起点本质上可能不存在，也不需要存在。假设的中性初始状态有利于人工或模拟计算，预计不会改变任何发现的普遍性。

3. 领域 Territory：一个有序系统应该有一个域，由系统发起的通用计算，将产生一个仍然在域内的最优解。

4. 达成模式 Reaching Pattern：在计算空间中的达成模式、或者在计算空间中的最优驱动达成模式的形式，主要依赖于计算空间下度量空间的性质和维度、以及实现可达的经验路径的惩罚和奖励规则。我们感兴趣的经验路径有五种基本形式：持续正向增强经验路径、持续负向增强经验路径、混合持续型经验路径、衰减规模经验路径和选择经验路径。

在选择体验路径的复合计算中，包括当前交互和滞后交互，动态拓扑转换 dynamic topological transformation，并暗示有序系统的体验路径中的不变性和方差特征。


同时，可达成最优的计算形式给出了复杂性模型、混沌性模型、和确定性模型之间的界限。当 “按件奖励”RAYG是最优选择计算，并且可达模式是持续正向经验路径、持续负向经验路径、或混合持久模式经验路径时，其底层计算应该是采用确定规则的简单系统计算。如果可达模式没有在 RAYG 体制中经历的持续模式，基础计算则提示有混沌系统。当最佳选择计算涉及非 RAYG 计算时，此为复杂性计算所驱动的复合效应。

著名学者

  • 罗伯特·麦考密克·亚当斯 Robert McCormick Adams
  • 斯图尔特 · 考夫曼 Stuart Kauffma
  • 克里斯托弗·亚历山大 Christopher Alexander
  • 大卫·克拉考尔 David Krakauer
  • 菲利普·安德森 Philip Anderson
  • 埃伦·利维 Ellen Levy
  • 肯尼思·阿诺 Kenneth Arrow
  • 罗伯特·梅 Robert May
  • 罗伯特·阿克塞尔罗德 Robert Axelrod
  • 梅拉妮·米歇尔 Melanie Mitchell
  • 布莱恩·阿瑟 W. Brian Arthur
  • 克里斯·摩尔 Cris Moore
  • 杨纳尔·巴亚姆 Yaneer Bar-Yam
  • 埃德加·莫林 Edgar Morin
  • 阿尔伯特·巴拉巴西 Albert-laszlo Barabasi
  • 哈罗德·莫罗维茨 Harold Morowitz
  • 格雷戈里 · 贝特森 Gregory Bateson
  • 斯科特·佩奇 Scott Page
  • 路德维希·冯·贝塔郎菲 Ludwig von Bertalanffy
  • 卢西亚诺·皮埃特罗内罗 Luciano Pietronero
  • 杰弗里·韦斯特 Geoffery West
  • 史蒂芬·沃尔弗拉姆 Stephen Wolfram
  • 邓肯·沃茨 Duncan J Watts
  • 阿尔弗雷德·布勒 Alfred Hübler
  • 默里·盖尔曼 Murray Gell-Mann
  • 约书亚·爱泼斯坦 Joshua Epstein
  • 约翰·霍兰德 John Holland
  • 杰·韦瑞特·弗瑞斯特 Jay Wright Forrester
  • 戴夫·斯诺登 Dave Snowden
  • 亚历山德罗·韦斯皮尼亚尼 Alessandro Vespignani

相关概念

  • 流程架构 Process architecture
  • 自组织 Self-organization
  • 社会学和复杂系统理论 Sociology and complexity science
  • 系统性事故 System accident
  • 系统动力学 System dynamics
  • 系统等效性 System equivalence
  • 系统理论 Systems theory
    • 人类学系统论 System theory in anthropology
  • 波动性、不确定性、复杂性、模糊性（VUCA) Volatility, uncertainty, complexity
    and ambiguity

进一步阅读

外部链接

参考文献

  1. ↑ Bar-Yam (2014) "General Features of Complex Systems".Yaneer, Encyclopedia of Life Support Systems. Retrieved 16 September.
  2. ↑ Daniel Dennett (1995), Darwin's Dangerous Idea, Penguin Books, London, ISBN 978-0-14-016734-4, ISBN 0-14-016734-X
  3. ↑ On the ‘complexity turn’ in planning: An adaptive rationale to navigate spaces and times of uncertainty 关于规划中的“复杂性转向” : 一个适应性的理论基础，用于导航不确定性的空间和时间。
  4. ↑ Alan Randall (2011). Risk and Precaution. Cambridge University Press. ISBN 9781139494793.
  5. ↑ S. V. Buldyrev; R. Parshani; G. Paul; H. E. Stanley; S. Havlin (2010). "Catastrophic cascade of failures in interdependent networks". Nature. 464 (7291): 1025–8. arXiv:0907.1182. Bibcode:2010Natur.464.1025B. doi:10.1038/nature08932. PMID 20393559
  6. ↑ Berezin, Yehiel; Bashan, Amir; Danziger, Michael M.; Li, Daqing; Havlin, Shlomo (2015). "Localized attacks on spatially embedded networks with dependencies". Scientific Reports. 5 (1): 8934. Bibcode:2015NatSR...5E8934B. doi:10.1038/srep08934. ISSN 2045-2322. PMC 4355725. PMID 25757572
  7. ↑ 7.0 7.1 Majdandzic, Antonio; Podobnik, Boris; Buldyrev, Sergey V.; Kenett, Dror Y.; Havlin, Shlomo; Eugene Stanley, H. (2013). "Spontaneous recovery in dynamical networks". Nature Physics. 10 (1): 34–38. Bibcode:2014NatPh..10...34M. doi:10.1038/nphys2819. ISSN 1745-2473.
  8. ↑ Lever, J. Jelle; Leemput, Ingrid A.; Weinans, Els; Quax, Rick; Dakos, Vasilis; Nes, Egbert H.; Bascompte, Jordi; Scheffer, Marten (10 November 2019). "Foreseeing the future of mutualistic communities beyond collapse". Ecology Letters. doi:10.1111/ele.13401. PMID 31707763.
  9. ↑ 9.0 9.1 Majdandzic, Antonio; Braunstein, Lidia A.; Curme, Chester; Vodenska, Irena; Levy-Carciente, Sary; Eugene Stanley, H.; Havlin, Shlomo (2016). "Multiple tipping points and optimal repairing in interacting networks". Nature Communications. 7: 10850. arXiv:1502.00244. Bibcode:2016NatCo...710850M. doi:10.1038/ncomms10850. ISSN 2041-1723. PMC 4773515. PMID 26926803.
  10. ↑ Bascompte, J.; Jordano, P.; Melian, C. J.; Olesen, J. M. (24 July 2003). "The nested assembly of plant-animal mutualistic networks". Proceedings of the National Academy of Sciences. 100 (16): 9383–9387. doi:10.1073/pnas.1633576100. PMC 170927. PMID 12881488.
  11. ↑ Saavedra, Serguei; Reed-Tsochas, Felix; Uzzi, Brian (January 2009). "A simple model of bipartite cooperation for ecological and organizational networks". Nature. 457 (7228): 463–466. doi:10.1038/nature07532. ISSN 1476-4687. PMID 19052545.
  12. ↑ Bastolla, Ugo; Fortuna, Miguel A.; Pascual-García, Alberto; Ferrera, Antonio; Luque, Bartolo; Bascompte, Jordi (April 2009). "The architecture of mutualistic networks minimizes competition and increases biodiversity". Nature. 458 (7241): 1018–1020. doi:10.1038/nature07950. ISSN 1476-4687. PMID 19396144.
  13. ↑ Lever, J. Jelle; Nes, Egbert H. van; Scheffer, Marten; Bascompte, Jordi (2014). "The sudden collapse of pollinator communities". Ecology Letters. 17 (3): 350–359. doi:10.1111/ele.12236. hdl:10261/91808. ISSN 1461-0248. PMID 24386999.
  14. ↑ A. L. Barab´asi, R. Albert (2002). "Statistical mechanics of complex networks". Reviews of Modern Physics. 74 (1): 47–94. arXiv:cond-mat/0106096. Bibcode:2002RvMP...74...47A. CiteSeerX 10.1.1.242.4753. doi:10.1103/RevModPhys.74.47
  15. ↑ M. Newman (2010). Networks: An Introduction. Oxford University Press. ISBN 978-0-19-920665-0.
  16. ↑ 16.0 16.1 Reuven Cohen, Shlomo Havlin (2010).Complex Networks: Structure, Robustness and Function. Cambridge University Press. ISBN 978-0-521-84156-6.
  17. ↑ Castellani, Brian, 2018, Map of the Complexity Sciences Art & Science Factory (expandable version)
  18. ↑ History of Complex Systems Archived 2007-11-23 at the 2007-11-23Wayback Machine
  19. ↑ Ferguson, Adam (1767). An Essay on the History of Civil Society. London: T. Cadell. Part the Third, Section II, p. 205.
  20. ↑ Friedrich Hayek, "The Results of Human Action but Not of Human Design" in New Studies in Philosophy, Politics, Economics, Chicago: University of Chicago Press, 1978, pp. 96–105.
  21. ↑ Bruce J. Caldwell, Popper and Hayek:Who influenced whom? Archived 2018-12-11 at the Wayback Machine, Karl Popper 2002 Centenary Congress, 2002.
  22. ↑ Friedrich von Hayek, The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology, The University of Chicago Press, 1952.
  23. ↑ Vemuri, V. (1978). Modeling of Complex Systems: An Introduction. New York: Academic Press. ISBN 978-0127165509.
  24. ↑ Ledford, H (2015). "How to solve the world's biggest problems". Nature. 525 (7569): 308–311. Bibcode:2015Natur.525..308L. doi:10.1038/525308a. PMID 26381968.
  25. ↑ "History | Santa Fe Institute". www.santafe.edu. Retrieved 2018-05-17.
  26. ↑ Waldrop, M. M. (1993). Complexity: The emerging science at the edge of order and chaos. Simon and Schuster.
  27. ↑ CSIS paper: "Organizing for a Complex World: The Way Ahead
  28. ↑ Forsman, Jonas; Moll, Rachel; Linder, Cedric (2014). "Extending the theoretical framing for physics education research: An illustrative application of complexity science". Physical Review Special Topics: Physics Education Research. 10 (2): 020122. Bibcode:2014PRPER..10b0122F. doi:10.1103/PhysRevSTPER.10.020122. http://hdl.handle.net/10613/2583.
  29. ↑ ["Reason Magazine - The Road from Serfdom" "Reason Magazine - The Road from Serfdom"]. Archived from the original on 2007-03-10. Retrieved 2017-09-22.
  30. ↑ Friedrich August von Hayek - Prize Lecture
  31. ↑ Hayles, N. K. (1991). Chaos Bound: Orderly Disorder in Contemporary Literature and Science. Cornell University Press, Ithaca, NY.
  32. ↑ Prigogine, I. (1997). The End of Certainty, The Free Press, New York.
  33. ↑ See also D. Carfì (2008). "Superpositions in Prigogine approach to irreversibility". AAPP: Physical, Mathematical, and Natural Sciences. 86 (1): 1–13.
  34. ↑ 34.0 34.1 Cilliers, P. (1998). Complexity and Postmodernism: Understanding Complex Systems, Routledge, London.
  35. ↑ Per Bak (1996). How Nature Works: The Science of Self-Organized Criticality, Copernicus, New York, U.S.c
  36. ↑ Colander, D. (2000). The Complexity Vision and the Teaching of Economics, E. Elgar, Northampton, Massachusetts.
  37. ↑ Buchanan, M. (2000). Ubiquity : Why catastrophes happen, three river press, New-York.
  38. ↑ Gell-Mann, M. (1995). What is Complexity? Complexity 1/1, 16-19
  39. ↑ Dorogovtsev, S.N.; Mendes, J.F.F. (2003). Evolution of Networks. Adv. Phys. 51. p. 1079. arXiv:cond-mat/0106144. doi:10.1093/acprof:oso/9780198515906.001.0001. ISBN 9780198515906.
  40. ↑ Fortunato, Santo (2011). "Reuven Cohen and Shlomo Havlin: Complex Networks". Journal of Statistical Physics. 142 (3): 640–641. Bibcode:2011JSP...142..640F. doi:10.1007/s10955-011-0129-7. ISSN 0022-4715.
  41. ↑ Newman, Mark (2010).Networks. doi:10.1093/acprof:oso/9780199206650.001.0001. ISBN 9780199206650.
  42. ↑ Cohen, Reuven; Erez, Keren; ben-Avraham, Daniel; Havlin, Shlomo (2001). "Cohen, Erez, ben-Avraham, and Havlin Reply". Physical Review Letters. 87 (21): 219802. Bibcode:2001PhRvL..87u9802C. doi:10.1103/PhysRevLett.87.219802. ISSN 0031-9007.
  43. ↑ Barrat, A.; Barthelemy, M.; Pastor-Satorras, R.; Vespignani, A. (2004). "The architecture of complex weighted networks". Proceedings of the National Academy of Sciences. 101 (11): 3747–3752. arXiv:cond-mat/0311416. Bibcode:2004PNAS..101.3747B. doi:10.1073/pnas.0400087101. ISSN 0027-8424. PMC 374315. PMID 15007165
  44. ↑ Yamasaki, K.; Gozolchiani, A.; Havlin, S. (2008). "Climate Networks around the Globe are Significantly Affected by El Niño". Physical Review Letters. 100 (22): 228501. Bibcode:2008PhRvL.100v8501Y. doi:10.1103/PhysRevLett.100.228501. ISSN 0031-9007. PMID 18643467.
  45. ↑ Gao, Jianxi; Buldyrev, Sergey V.; Stanley, H. Eugene; Havlin, Shlomo (2011)."Networks formed from interdependent networks" (PDF). Nature Physics. 8 (1): 40–48. Bibcode:2012NatPh...8...40G. CiteSeerX 10.1.1.379.8214. doi:10.1038/nphys2180. ISSN 1745-2473.
  46. ↑ Li, Daqing; Fu, Bowen; Wang, Yunpeng; Lu, Guangquan; Berezin, Yehiel; Stanley, H. Eugene; Havlin, Shlomo (2015-01-20). "Percolation transition in dynamical traffic network with evolving critical bottlenecks". Proceedings of the National Academy of Sciences. 112 (3): 669–672. Bibcode:2015PNAS..112..669L. doi:10.1073/pnas.1419185112. ISSN 0027-8424. PMC 4311803. PMID 25552558
  47. ↑ Limiao Zhang, Guanwen Zeng; Daqing Li, Hai-Jun Huang; H Eugene Stanley, Shlomo Havlin (2019). "Scale-free resilience of real traffic jams". Proceedings of the National Academy of Sciences. 116 (18): 8673–8678. arXiv:1804.11047. Bibcode:2019PNAS..116.8673Z. doi:10.1073/pnas.1814982116. PMC 6500150. PMID 30979803
  48. ↑ Battiston, Stefano; Caldarelli, Guido; May, Robert M.; Roukny, tarik; Stiglitz, Joseph E. (2016-09-06). "The price of complexity in financial networks". Proceedings of the National Academy of Sciences. 113 (36): 10031–10036. Bibcode:2016PNAS..11310031B. doi:10.1073/pnas.1521573113. PMC 5018742. PMID 27555583.
  49. ↑ Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. ISBN 978-1507658246. Chapter 4.

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电子书《复杂》下载 by <美>梅拉妮•米歇尔（Melanie Mitchell）
美国新英格兰复杂系统研究所（New England Complex Systems Institute, NECSI）的 Yaneer Bar-Yam（创始人及所长）和 Alexander F. Siegenfeld 近期写的一篇综述，梳理了复杂性研究的共识，全面介绍了复杂系统科学这一领域的基本原理、常用方法和应用方向。集智俱乐部对此进行了翻译整理。新英格兰复杂系统研究所长文综述：复杂系统科学及其应用
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系统科学导引（一）：概论部分
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  • 复杂系统科普入门： 复杂 Complexity 梅拉妮·米歇尔 Melanie Mitchell
梅拉妮是道格拉斯·侯世达 Douglas Hofstadter的学生，目前在波特兰大学执教。主要工作方向是类比推理、复杂系统、基因算法与元胞自动机。《复杂》自2009出版后，一路好评，豆瓣评分9分。从起源、演进、定义、度量几个方面介绍什么是复杂系统。


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