“混沌边缘”的版本间的差异

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The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.
 
The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.
  
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混沌边缘定义为有序和无序之间的过渡空间，这种空间被假设存在于各种各样的系统中。这个过渡区在有序和无序之间产生了恒定的动态相互作用，是一个有界不稳定区域。
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混沌边缘是有序和无序之间的过渡空间，这种空间被假设存在于各种各样的系统中。混沌边缘是一个有界的不稳定区域，不断地发生着有序和无序之间的动态相互作用。
 
--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+可补充：
 
--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+可补充：
 
一个能出现复杂现象的系统往往具有很大的自由度数目，由于非线性的存在，导致在高维相空间中存在一个有很多大于零的Lyapunov特征指数的奇怪吸引子。在这样的奇怪吸引子中存在数目巨大的有序成分和各种各样反映为物理空间有结构、时间上为混沌的成分，这些成分在通常意义下为不稳定。一旦受到某种刺激，按照混沌控制思想及其尚不知原因的原理，很快地、自适应地选择目标并达到目标，这样就导致了各种复杂现象的产生.由于这些成分构成奇怪吸引子中的一个稠集，因而对于目标响应是非常敏感的，这就导致某种不可预测性存在。--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+
 
一个能出现复杂现象的系统往往具有很大的自由度数目，由于非线性的存在，导致在高维相空间中存在一个有很多大于零的Lyapunov特征指数的奇怪吸引子。在这样的奇怪吸引子中存在数目巨大的有序成分和各种各样反映为物理空间有结构、时间上为混沌的成分，这些成分在通常意义下为不稳定。一旦受到某种刺激，按照混沌控制思想及其尚不知原因的原理，很快地、自适应地选择目标并达到目标，这样就导致了各种复杂现象的产生.由于这些成分构成奇怪吸引子中的一个稠集，因而对于目标响应是非常敏感的，这就导致某种不可预测性存在。--[[用户:沐晨|沐晨]]（[[用户讨论:沐晨|讨论]]）+
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The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA). As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation.  At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.
 
The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA). As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation.  At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.
  
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数学家'''Doyne Farmer'''提出了混沌一词，将其用于描述计算机科学家'''克里斯托弗·兰顿Christopher Langton'''发现的过渡现象。该短语最初指的是变量λ范围内的区域，该区域随着检查'''元胞自动机（CA）'''的行为发生变化。随着λ变化，CA的行为经历了行为的相变。兰顿发现了一个有利于生产具有通用计算能力CAs的小区域。大约在同一时间，物理学家'''詹姆士·克劳奇菲尔德James P. Crutchfield'''和其他人开始使用混沌来描述或多或少相同的概念。
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混沌边缘一词由数学家'''Doyne Farmer'''提出，用于描述计算机科学家'''克里斯托弗·兰顿Christopher Langton'''发现的过渡现象。混沌边缘最初指的是变量λ范围内的区域，在该区域内观察'''元胞自动机（CA）'''的行为发生变化。随着λ变化，元胞自动机的行为发生了相变。兰顿发现了一个有利于生产具有通用计算能力的元胞自动机的小区域。大约在同一时间，物理学家'''詹姆士·克劳奇菲尔德James P. Crutchfield'''和其他人开始使用混沌边缘（onset of chaos）来描述这一大致相同的概念。
  
  
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In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social  systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal. The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others.  The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.
 
In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social  systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal. The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others.  The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.
  
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在一般的科学中，该短语是指一个比喻，即某些物理、生物、经济、社会系统在有序、完全随机、混乱之间的区域内运行，其中复杂性是最大化的。但是'''梅勒妮 · 米切尔Melanie Mitchell'''等人对此概念的普遍性及意义提出了质疑。工商界也借用了该短语，不过时常使用的并不恰当，常在远超出该词原有含义范围的情况下使用。
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一般在科学领域，混沌边缘一词用于形容某些物理、生物、经济、社会系统在或有序或完全随机或混沌的状态间运行，其中复杂性是最大化的。但是'''梅勒妮 · 米切尔Melanie Mitchell'''等人对此概念的普遍性及意义提出了质疑。工商界也借用了这个词，不过时常使用的并不恰当，常在远超出该词原有含义范围的情况下使用。
  
  
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适应对所有生物和系统都起着至关重要的作用。为了更好地适应当前环境，它们都在不断改变其内在属性。自适应最重要的工具是许多自然系统固有的自我调节参数。具有自调整参数的系统具有避免混沌的显著特征。这种现象称为“适应混沌的边缘”。
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适应对所有生物和系统都起着至关重要的作用。为了更好地适应当前环境，它们都在不断改变其内在属性。自适应最重要的工具是许多自然系统所固有的自调整参数。具有自调整参数的系统具有避免混沌的显著特征。这种现象称为“混沌边缘的适应性”。
  
  
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Adaptation to the edge of chaos refers to the idea that many complex adaptive systems seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics has shown that edge of chaos is the optimal settings for control of a system. It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.
 
Adaptation to the edge of chaos refers to the idea that many complex adaptive systems seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics has shown that edge of chaos is the optimal settings for control of a system. It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.
  
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混沌边缘的适应性，是指许多复杂的自适应系统似乎直观地朝着混沌与秩序之间的边界发展。物理学已经表明，混沌边缘是控制系统的最佳设置，同时它也是一个可选设置，可以影响物理系统执行基本功能的计算能力。
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许多复杂的自适应系统似乎在直观地朝着混沌与秩序之间的边界进化，这种行为被称为适应混沌边缘。物理学已经表明，混沌边缘是控制系统的最佳设置，同时它也是一个可选设置，可以影响物理系统执行基本功能的计算能力。
 
  
  
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由于适应在许多自然系统中的重要性，混沌边缘的适应因此在许多科学研究中占有重要地位。物理学家证明了在元胞自动机规则的种群中发生了对混沌和有序边界状态的适应，这些规则通过遗传算法优化了性能。雪崩模型和地震模型中的自组织临界性就是很好的说明。
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由于适应在许多自然系统中的重要性，因此，混沌边缘的适应性在许多科学研究中占据重要地位。物理学家证明，对混沌秩序边缘的状态的适应发生在具有细胞自动机规则的种群中，这些规则自动优化了遗传算法的性能。雪崩模型和地震模型中的自组织临界性就是很好的说明。
  
  
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The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos. Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.
 
The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos. Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.
  
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最简单的混沌动力学模型是逻辑斯蒂映射。自调整逻辑映射动力学表现出对混沌边缘的适应性。理论分析可以预测在系统演化边界附近的窄参数区域位置。
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最简单的混沌动力学模型是逻辑斯蒂映射。自调整的逻辑映射动力学表现出对混沌边缘的适应性。理论分析可以预测在系统演化边界附近的窄参数区域位置。
  
  

2020年7月19日 (日) 23:30的版本

此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。

For the computer game, see Independence War 2: Edge of Chaos.


文件:Shish-kebab-skewer-60458 640.jpg
“The truly creative changes and the big shifts occur right at the edge of chaos,” said Dr. Robert Bilder, a psychiatry and psychology professor at UCLA's Semel Institute for Neuroscience and Human Behavior.[1]
文件:Shish-kebab-skewer-60458 640.jpg
“The truly creative changes and the big shifts occur right at the edge of chaos,” said Dr. Robert Bilder, a psychiatry and psychology professor at UCLA's Semel Institute for Neuroscience and Human Behavior. [文件: shish-kebab-skewer-60458640。 加州大学洛杉矶分校塞梅尔神经科学和人类行为研究所的精神病学和心理学教授罗伯特 · 比尔德Robert Bilder博士说: “真正具有创造性的变化和巨大的转变就发生在混沌边缘。

]]


The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.[2]

The edge of chaos is a transition space between order and disorder that is hypothesized to exist within a wide variety of systems. This transition zone is a region of bounded instability that engenders a constant dynamic interplay between order and disorder.

混沌边缘是有序和无序之间的过渡空间，这种空间被假设存在于各种各样的系统中。混沌边缘是一个有界的不稳定区域，不断地发生着有序和无序之间的动态相互作用。 --沐晨（讨论）+可补充： 一个能出现复杂现象的系统往往具有很大的自由度数目，由于非线性的存在，导致在高维相空间中存在一个有很多大于零的Lyapunov特征指数的奇怪吸引子。在这样的奇怪吸引子中存在数目巨大的有序成分和各种各样反映为物理空间有结构、时间上为混沌的成分，这些成分在通常意义下为不稳定。一旦受到某种刺激，按照混沌控制思想及其尚不知原因的原理，很快地、自适应地选择目标并达到目标，这样就导致了各种复杂现象的产生.由于这些成分构成奇怪吸引子中的一个稠集，因而对于目标响应是非常敏感的，这就导致某种不可预测性存在。--沐晨（讨论）+


Even though the idea of the edge of chaos is abstract and unintuitive, it has many applications in such fields as ecology,[3] business management,[4] psychology,[5] political science, and other domains of the social science. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.[6]

Even though the idea of the edge of chaos is abstract and unintuitive, it has many applications in such fields as ecology, business management, psychology, political science, and other domains of the social science. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.

尽管混沌边缘的概念十分抽象且不直观，但它确实在生态学、商业管理、心理学、政治科学、社会科学等领域具有诸多应用。物理学家发现几乎所有具有反馈的系统都会对混沌边缘产生适应行为。


History 历史

模板:Unreferenced section

The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA). As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.

The phrase edge of chaos was coined by mathematician Doyne Farmer to describe the transition phenomenon discovered by computer scientist Christopher Langton. The phrase originally refers to an area in the range of a variable, λ (lambda), which was varied while examining the behavior of a cellular automaton (CA). As λ varied, the behavior of the CA went through a phase transition of behaviors. Langton found a small area conducive to produce CAs capable of universal computation. At around the same time physicist James P. Crutchfield and others used the phrase onset of chaos to describe more or less the same concept.

混沌边缘一词由数学家Doyne Farmer提出，用于描述计算机科学家克里斯托弗·兰顿Christopher Langton发现的过渡现象。混沌边缘最初指的是变量λ范围内的区域，在该区域内观察元胞自动机（CA）的行为发生变化。随着λ变化，元胞自动机的行为发生了相变。兰顿发现了一个有利于生产具有通用计算能力的元胞自动机的小区域。大约在同一时间，物理学家詹姆士·克劳奇菲尔德James P. Crutchfield和其他人开始使用混沌边缘（onset of chaos）来描述这一大致相同的概念。


In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal. The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others. The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.

In the sciences in general, the phrase has come to refer to a metaphor that some physical, biological, economic and social systems operate in a region between order and either complete randomness or chaos, where the complexity is maximal. The generality and significance of the idea, however, has since been called into question by Melanie Mitchell and others. The phrase has also been borrowed by the business community and is sometimes used inappropriately and in contexts that are far from the original scope of the meaning of the term.

一般在科学领域，混沌边缘一词用于形容某些物理、生物、经济、社会系统在或有序或完全随机或混沌的状态间运行，其中复杂性是最大化的。但是梅勒妮 · 米切尔Melanie Mitchell等人对此概念的普遍性及意义提出了质疑。工商界也借用了这个词，不过时常使用的并不恰当，常在远超出该词原有含义范围的情况下使用。


Stuart Kauffman has studied mathematical models of evolving systems in which the rate of evolution is maximized near the edge of chaos.

Stuart Kauffman has studied mathematical models of evolving systems in which the rate of evolution is maximized near the edge of chaos.

斯图尔特·考夫曼Stuart Kauffman研究了进化系统的数学模型，其中进化速率在混沌边缘附近达到最大。


Adaptation 适应

Adaptation plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment.[7] The most important instruments for the adaptation are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".

Adaptation plays a vital role for all living organisms and systems. All of them are constantly changing their inner properties to better fit in the current environment. The most important instruments for the adaptation are the self-adjusting parameters inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".


适应对所有生物和系统都起着至关重要的作用。为了更好地适应当前环境，它们都在不断改变其内在属性。自适应最重要的工具是许多自然系统所固有的自调整参数。具有自调整参数的系统具有避免混沌的显著特征。这种现象称为“混沌边缘的适应性”。


Adaptation to the edge of chaos refers to the idea that many complex adaptive systems seem to intuitively evolve toward a regime near the boundary between chaos and order.[8] Physics has shown that edge of chaos is the optimal settings for control of a system.[9] It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.[10]

Adaptation to the edge of chaos refers to the idea that many complex adaptive systems seem to intuitively evolve toward a regime near the boundary between chaos and order. Physics has shown that edge of chaos is the optimal settings for control of a system. It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.

混沌边缘的适应性，是指许多复杂的自适应系统似乎直观地朝着混沌与秩序之间的边界发展。物理学已经表明，混沌边缘是控制系统的最佳设置，同时它也是一个可选设置，可以影响物理系统执行基本功能的计算能力。


Because of the importance of adaptation in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of cellular automata rules which optimize the performance evolving with a genetic algorithm.[11][12] Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.[13]

Because of the importance of adaptation in many natural systems, adaptation to the edge of the chaos takes a prominent position in many scientific researches. Physicists demonstrated that adaptation to state at the boundary of chaos and order occurs in population of cellular automata rules which optimize the performance evolving with a genetic algorithm. Another example of this phenomenon is the self-organized criticality in avalanche and earthquake models.


由于适应在许多自然系统中的重要性，因此，混沌边缘的适应性在许多科学研究中占据重要地位。物理学家证明，对混沌秩序边缘的状态的适应发生在具有细胞自动机规则的种群中，这些规则自动优化了遗传算法的性能。雪崩模型和地震模型中的自组织临界性就是很好的说明。


The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos.[14] Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.[15]

The simplest model for chaotic dynamics is the logistic map. Self-adjusting logistic map dynamics exhibit adaptation to the edge of chaos. Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.

最简单的混沌动力学模型是逻辑斯蒂映射。自调整的逻辑映射动力学表现出对混沌边缘的适应性。理论分析可以预测在系统演化边界附近的窄参数区域位置。


See also 进一步阅读

References 参考资料

  1. ↑ Schwartz, K. (2014). "On the Edge of Chaos: Where Creativity Flourishes". KOED.
  2. ↑ Complexity Labs. "Edge of Chaos". Complexity Labs. Retrieved August 24, 2016.
  3. ↑ Ranjit Kumar Upadhyay (2009). "Dynamics of an ecological model living on the edge of chaos". Applied Mathematics and Computation. 210 (2): 455–464. doi:10.1016/j.amc.2009.01.006.
  4. ↑ Deragon, Jay. "Managing On The Edge Of Chaos". Relationship Economy.
  5. ↑ Lawler, E.; Thye, S.; Yoon, J. (2015). Order on the Edge of Chaos Social Psychology and the Problem of Social Order. Cambridge University Press. ISBN 9781107433977. 
  6. ↑ Wotherspoon, T.; et., al. (2009). "Adaptation to the edge of chaos with random-wavelet feedback". J. Phys. Chem. A. 113 (1): 19–22. Bibcode:2009JPCA..113...19W. doi:10.1021/jp804420g. PMID 19072712.
  7. ↑ Strogatz, Steven (1994). Nonlinear dynamics and Chaos. Westview Press. 
  8. ↑ Kauffman, S.A. (1993). The Origins of Order Self-Organization and Selection in Evolution. New York: Oxford University Press. ISBN 9780195079517. 
  9. ↑ Pierre, D.; et., al. (1994). "A theory for adaptation and competition applied to logistic map dynamics". Physica D. 75 (1–3): 343–360. Bibcode:1994PhyD...75..343P. doi:10.1016/0167-2789(94)90292-5.
  10. ↑ Langton, C.A. (1990). "Computation at the edge of chaos". Physica D. 42 (1–3): 12. Bibcode:1990PhyD...42...12L. doi:10.1016/0167-2789(90)90064-v.
  11. ↑ Packard, N.H. (1988). "Adaptation toward the edge of chaos". Dynamic Patterns in Complex Systems: 293–301.
  12. ↑ Mitchell, M.; Hraber, P.; Crutchfield, J. (1993). "Revisiting the edge of chaos: Evolving cellular automata to perform computations". Complex Systems. 7 (2): 89–130. arXiv:adap-org/9303003. Bibcode:1993adap.org..3003M.
  13. ↑ Bak, P.; Tang, C.; Wiesenfeld, K. (1988). "Self-organized criticality". Phys Rev A. 38 (1): 364–374. Bibcode:1988PhRvA..38..364B. doi:10.1103/PhysRevA.38.364.
  14. ↑ Melby, P.; et., al. (2000). "Adaptation to the edge of chaos in the self-adjusting logistic map". Phys. Rev. Lett. 84 (26): 5991–5993. arXiv:nlin/0007006. Bibcode:2000PhRvL..84.5991M. doi:10.1103/PhysRevLett.84.5991. PMID 10991106.
  15. ↑ Bayam, M.; et., al. (2006). "Conserved quantities and adaptation to the edge of chaos". Physical Review E. 73 (5): 056210. Bibcode:2006PhRvE..73e6210B. doi:10.1103/PhysRevE.73.056210.
  • Origins of Order: Self-Organization and Selection in Evolution by Stuart Kauffman


External links 外部链接


模板:Chaos theory

Category:Chaos theory

范畴: 混沌理论

Category:Self-organization

类别: 自我组织


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