863
个编辑
更改
跳到导航
跳到搜索
第11行：
第11行： − − {{Unreferenced section|date=March 2017}} − − 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 (programming)|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. − − − In the sciences in general, the phrase has come to refer to a metaphor that some [[physics|physical]], [[biology|biological]], [[economics|economic]] and [[sociology|social]] [[system]]s operate in a region between order and either complete [[randomness]] or [[chaos theory|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. − − [[Stuart Kauffman]] has studied [[mathematical model]]s of [[evolution|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. − + − − [[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.<ref>{{cite book|last1=Strogatz|first1=Steven|title=Nonlinear dynamics and Chaos|date=1994|publisher=[[Westview Press]]}}</ref> The most important instruments for the [[adaptation]] are the [[adaptive systems|self-adjusting parameters]] inherent for many natural systems. The prominent feature of systems with self-adjusting parameters is an ability to avoid [[chaos theory|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.<ref>{{cite book|last1=Kauffman|first1=S.A.|title=The Origins of Order Self-Organization and Selection in Evolution|date=1993|publisher=[[Oxford University Press]]|location=New York|isbn=9780195079517}}</ref> Physics has shown that edge of chaos is the optimal settings for control of a system.<ref>{{cite journal|last1=Pierre|first1=D.|last2=et.|first2=al.|title=A theory for adaptation and competition applied to logistic map dynamics|journal=Physica D|date=1994|volume=75|issue=1–3|pages=343–360|bibcode=1994PhyD...75..343P|doi=10.1016/0167-2789(94)90292-5}}</ref> It is also an optional setting that can influence the ability of a physical system to perform primitive functions for computation.<ref>{{cite journal|last1=Langton|first1=C.A.|title=Computation at the edge of chaos|journal=Physica D|date=1990|volume=42|issue=1–3|pages=12|doi=10.1016/0167-2789(90)90064-v|bibcode=1990PhyD...42...12L|url=https://zenodo.org/record/1258375}}</ref> − − 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]].<ref>{{cite journal|last1=Packard|first1=N.H.|title=Adaptation toward the edge of chaos|journal=Dynamic Patterns in Complex Systems|date=1988|pages=293–301}}</ref><ref>{{cite journal|last1=Mitchell|first1=M.|last2=Hraber|first2=P.|last3=Crutchfield|first3=J.|title=Revisiting the edge of chaos: Evolving cellular automata to perform computations|journal=Complex Systems|date=1993|volume=7|issue=2|pages=89–130|arxiv=adap-org/9303003|bibcode=1993adap.org..3003M}}</ref> Another example of this phenomenon is the [[self-organized criticality]] in [[avalanche]] and earthquake models.<ref>{{cite journal|last1=Bak|first1=P.|last2=Tang|first2=C.|last3=Wiesenfeld|first3=K.|title=Self-organized criticality|journal=Phys Rev A|date=1988|volume=38|issue=1|pages=364–374|doi=10.1103/PhysRevA.38.364|bibcode=1988PhRvA..38..364B}}</ref> − 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.<ref>{{cite journal|last1=Melby|first1=P.|last2=et.|first2=al.|title=Adaptation to the edge of chaos in the self-adjusting logistic map.|journal=Phys. Rev. Lett.|date=2000|doi=10.1103/PhysRevLett.84.5991|arxiv=nlin/0007006|bibcode=2000PhRvL..84.5991M|volume=84|issue=26|pages=5991–5993|pmid=10991106}}</ref> Theoretical analysis allowed prediction of the location of the narrow parameter regime near the boundary to which the system evolves.<ref>{{cite journal|last1=Bayam|first1=M.|last2=et.|first2=al.|title=Conserved quantities and adaptation to the edge of chaos|journal=Physical Review E|date=2006|volume=73|issue=5|pages=056210|doi=10.1103/PhysRevE.73.056210|bibcode=2006PhRvE..73e6210B}}</ref>+ − 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。 − +
无编辑摘要
== 历史 ==
== 历史 ==
混沌边缘一词是由数学家'''Doyne Farmer'''提出，用于描述计算机科学家'''克里斯托弗·朗顿Christopher Langton'''发现的过渡现象。混沌边缘最初是指变量λ的区间，在该区间内观察'''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产生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。
混沌边缘一词是由数学家'''Doyne Farmer'''提出，用于描述计算机科学家'''克里斯托弗·朗顿Christopher Langton'''发现的过渡现象。混沌边缘最初是指变量λ的区间，在该区间内观察'''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产生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。
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'''梅拉妮·米歇尔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。
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'''梅拉妮·米歇尔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。
'''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。
'''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==
== 适应 ==
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，<ref>{{cite book|last1=Strogatz|first1=Steven|title=Nonlinear dynamics and Chaos|date=1994|publisher=[[Westview Press]]}}</ref> 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”。
.
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<ref>{{cite journal|last1=Pierre|first1=D.|last2=et.|first2=al.|title=A theory for adaptation and competition applied to logistic map dynamics|journal=Physica D|date=1994|volume=75|issue=1–3|pages=343–360|bibcode=1994PhyD...75..343P|doi=10.1016/0167-2789(94)90292-5}}</ref>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。<ref>{{cite journal|last1=Langton|first1=C.A.|title=Computation at the edge of chaos|journal=Physica D|date=1990|volume=42|issue=1–3|pages=12|doi=10.1016/0167-2789(90)90064-v|bibcode=1990PhyD...42...12L|url=https://zenodo.org/record/1258375}}</ref>
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<ref>{{cite journal|last1=Packard|first1=N.H.|title=Adaptation toward the edge of chaos|journal=Dynamic Patterns in Complex Systems|date=1988|pages=293–301}}</ref>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。<ref>{{cite journal|last1=Bak|first1=P.|last2=Tang|first2=C.|last3=Wiesenfeld|first3=K.|title=Self-organized criticality|journal=Phys Rev A|date=1988|volume=38|issue=1|pages=364–374|doi=10.1103/PhysRevA.38.364|bibcode=1988PhRvA..38..364B}}</ref>
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。<ref>{{cite journal|last1=Melby|first1=P.|last2=et.|first2=al.|title=Adaptation to the edge of chaos in the self-adjusting logistic map.|journal=Phys. Rev. Lett.|date=2000|doi=10.1103/PhysRevLett.84.5991|arxiv=nlin/0007006|bibcode=2000PhRvL..84.5991M|volume=84|issue=26|pages=5991–5993|pmid=10991106}}</ref>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。<ref>{{cite journal|last1=Bayam|first1=M.|last2=et.|first2=al.|title=Conserved quantities and adaptation to the edge of chaos|journal=Physical Review E|date=2006|volume=73|issue=5|pages=056210|doi=10.1103/PhysRevE.73.056210|bibcode=2006PhRvE..73e6210B}}</ref>
==See also 进一步阅读==
==进一步阅读==
* [[Self-organized criticality]]
* [[Self-organized criticality]]