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第9行：
第9行： − + 第23行：
第23行： − 混沌的边缘是有序和无序之间的过渡空间，这种过渡空间被假设存在于各种各样的系统中。这个过渡区域是一个有界的不稳定区域，在有序和无序之间产生持续的动态相互作用。+ 第31行：
第31行： − 尽管混沌边缘的概念是抽象的和不直观的，但它在生态学、商业管理、心理学、政治科学和其他社会科学领域有许多应用。物理学家已经证明，对混沌边缘的适应几乎发生在所有具有反馈的系统中。+ − + 第43行：
第43行： − 混沌的边缘这个短语是由数学家 Doyne Farmer 创造的，用来描述由计算机科学家克里斯托弗·兰顿发现的转变现象。这个短语最初指的是变量(lambda)范围内的一个区域，在检查一个细胞自动机(CA)的行为时，这个区域是不同的。不同的 CA 行为都经历了行为的相变。Langton 发现了一个很小的区域，有利于产生具有通用计算能力的 ca。大约在同一时期，物理学家詹姆斯 · p · 克拉奇菲尔德和其他人使用混沌开始这个短语来描述或多或少相同的概念。+ − 第51行：
第50行： − 在一般的科学中，这个短语已经变成了一个比喻，一些物理的、生物的、经济的和社会的系统运行在一个介于有序和完全随机或混乱之间的区域，其中复杂性是最大的。然而，这个想法的普遍性和重要性从那时起就受到了梅勒妮 · 米切尔和其他人的质疑。这个短语也被工商界借用，有时用得不恰当，而且用在远远超出该词原有含义范围的情况下。+ − 第59行：
第57行： − 斯图尔特 · 考夫曼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值。+ − + 第69行：
第67行： − 适应对所有生物体和系统都起着至关重要的作用。它们都在不断地改变自己的内在属性，以便更好地适应当前的环境。自适应最重要的手段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的显著特征是具有避免混沌的能力。这种现象的名称是“适应混沌的边缘”。+ + 第77行：
第76行： − 适应混沌的边缘是指这样的想法，许多复杂的自适应系统似乎直观地进化到一个制度接近混沌和秩序之间的边界。物理学已经表明，混沌边缘是系统控制的最佳设置。它也是一个可选的设置，可以影响物理系统执行基本功能的计算能力。 + 第85行：
第84行： − 由于适应在许多自然系统中的重要性，对混沌边缘的适应在许多科学研究中占有突出的地位。物理学家证明了元胞自动机规则种群对混沌和有序边界状态的适应性，该规则通过遗传算法优化性能演化。这种现象的另一个例子是雪崩和地震模型中的自组织临界性。 + 第93行：
第92行： − 混沌动力学最简单的模型是逻辑斯谛映射。自调整逻辑映射动力学表现出对混沌边缘的适应性。理论分析允许预测系统演化的边界附近窄参数区域的位置。+ − − + 第103行：
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无编辑摘要
[[File:Shish-kebab-skewer-60458 640.jpg|thumb|“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.
[[File:Shish-kebab-skewer-60458 640.jpg|thumb|“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的边缘。
[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.
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。
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.
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 ==
== History 历史==
{{Unreferenced section|date=March 2017}}
{{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, 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.
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。
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.
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。
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==
==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.<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.<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".
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”。
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.
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。
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.
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，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。
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.
最简单的混沌动力学模型是逻辑映射。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。
==See also==
==See also 也可以看看==
* [[Self-organized criticality]]
* [[Self-organized criticality]]
==References==
==References 参考资料==
{{Reflist}}
{{Reflist}}
== External links ==
== External links 外部链接==
* [http://bactra.org/notebooks/edge-of-chaos.html "The Edge of Chaos"] – a criticism of the idea's prevalence.
* [http://bactra.org/notebooks/edge-of-chaos.html "The Edge of Chaos"] – a criticism of the idea's prevalence.