混沌边缘

[[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.^[1]

[[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。

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^[2]。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。

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^[3]、商业管理^[4]、心理学^[5] 、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适应混沌边缘。^[6]

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。

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。

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，^[7] 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^[8]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。^[9]

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^[10]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。^[11]

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。^[12]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。^[13]

进一步阅读

Self-organized criticality

参考资料

↑ Schwartz, K. (2014). "On the Edge of Chaos: Where Creativity Flourishes". KOED.
↑ Complexity Labs. "Edge of Chaos". Complexity Labs. Retrieved August 24, 2016.
↑ 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.
↑ Deragon, Jay. "Managing On The Edge Of Chaos". Relationship Economy.
↑ 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.
↑ 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.
↑ Strogatz, Steven (1994). Nonlinear dynamics and Chaos. Westview Press.
↑ 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.
↑ 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.
↑ Packard, N.H. (1988). "Adaptation toward the edge of chaos". Dynamic Patterns in Complex Systems: 293–301.
↑ 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.
↑ 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.
↑ 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.

Christopher G. Langton (1990). "Computation at the edge of chaos" (PDF). Physica D. 42: 12. Bibcode:1990PhyD...42...12L. doi:10.1016/0167-2789(90)90064-V.

J. P. Crutchfield and K. Young (1990). "Computation at the Onset of Chaos". In W. Zurek. Entropy, Complexity, and the Physics of Information. SFI Studies in the Sciences of Complexity, VIII. Reading, Massachusetts: Addison-Wesley. pp. 223–269. http://csc.ucdavis.edu/~cmg/papers/CompOnset.pdf.

Mitchell, Melanie; Hraber, Peter T.; Crutchfield, James P. (1993). "Revisiting the edge of chaos: Evolving cellular automata to perform computations" (PDF). Complex Systems. 7: 89–130.

Melanie Mitchell, James P. Crutchfield and Peter T. Hraber. Dynamics, Computation, and the "Edge of Chaos": A Re-Examination

Origins of Order: Self-Organization and Selection in Evolution by Stuart Kauffman

Mora, Thierry; Bialek, William (2010). "Are biological systems poised at criticality?". Journal of Statistical Physics. 144 (2): 268–302. arXiv:1012.2242. Bibcode:2011JSP...144..268M. doi:10.1007/s10955-011-0229-4.

外部链接

"The Edge of Chaos" – a criticism of the idea's prevalence.

模板:Chaos theory

Category:Chaos theory

范畴: 混沌理论

Category:Self-organization

类别: 自我组织

This page was moved from wikipedia:en:Edge of chaos. Its edit history can be viewed at 混沌边缘/edithistory

[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] 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.

[9] 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.

[10] Packard, N.H. (1988). "Adaptation toward the edge of chaos". Dynamic Patterns in Complex Systems: 293–301.

[11] 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.

[12] 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.

[13] 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.

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