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]}
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]}
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✪ Edge of Chaos

✪ The Edge of Chaos
Transcription
Contents
History
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 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 models of evolving systems in which the rate of evolution is maximized near the edge of chaos.
Adaptation
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 selfadjusting parameters inherent for many natural systems. The prominent feature of systems with selfadjusting parameters is an ability to avoid chaos. The name for this phenomenon is "Adaptation to the edge of chaos".
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 have 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]}
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 selforganized criticality in avalanche and earthquake models.^{[13]}
The simplest model for chaotic dynamics is the logistic map. Selfadjusting 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]}
See also
References
 ^ 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 randomwavelet feedback". J. Phys. Chem. A. 113 (1): 19–22. Bibcode:2009JPCA..113...19W. doi:10.1021/jp804420g.
 ^ Strogatz, Steven (1994). Nonlinear dynamics and Chaos. Westview Press.
 ^ Kauffman, S.A. (1993). The Origins of Order SelfOrganization and Selection in Evolution. New York: Oxford University Press. ISBN 9780195079517.
 ^ 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:10.1016/01672789(94)902925.
 ^ Langton, C.A. (1990). "Computation at the edge of chaos". Physica D. 42 (1–3): 12. Bibcode:1990PhyD...42...12L. doi:10.1016/01672789(90)90064v.
 ^ Packard, N.H. (1988). "Adaptation toward the edge of chaos". Dynamic Patterns in Complex Systems: 293–301.
 ^ 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:adaporg/9303003. Bibcode:1993adap.org..3003M.
 ^ Bak, P.; Tang, C.; Wiesenfeld, K. (1988). "Selforganized 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 selfadjusting logistic map". Phys. Rev. Lett. 84 (26): 5991–5993. arXiv:nlin/0007006. Bibcode:2000PhRvL..84.5991M. doi:10.1103/PhysRevLett.84.5991.
 ^ 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:10.1016/01672789(90)90064V.
 J. P. Crutchfield and K. Young (1990). "Computation at the Onset of Chaos" (PDF). In W. Zurek (ed.). Entropy, Complexity, and the Physics of Information. SFI Studies in the Sciences of Complexity, VIII. Reading, Massachusetts: AddisonWesley. pp. 223–269.
 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 ReExamination
 Origins of Order: SelfOrganization 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/s1095501102294.
External links
 "The Edge of Chaos" – a criticism of the idea's prevalence.