Editing Complex system (section)

===Complexity and chaos theory===
Complex systems theory is related to [[chaos theory]], which in turn has its origins more than a century ago in the work of the French mathematician [[Henri Poincaré]]. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order.<ref>Hayles, N. K. (1991). ''[https://books.google.com/books?id=9g9QDwAAQBAJ&pg=PR7 Chaos Bound: Orderly Disorder in Contemporary Literature and Science]''. Cornell University Press, Ithaca, NY.</ref> Chaotic systems remain deterministic, though their long-term behavior can be difficult to predict with any accuracy. With perfect knowledge of the initial conditions and the relevant equations describing the chaotic system's behavior, one can theoretically make perfectly accurate predictions of the system, though in practice this is impossible to do with arbitrary accuracy.

The emergence of complex systems theory shows a domain between deterministic order and randomness which is complex.<ref name="PC98">[[Paul Cilliers|Cilliers, P.]] (1998). ''Complexity and Postmodernism: Understanding Complex Systems'', Routledge, London.</ref> This is referred to as the "[[edge of chaos]]".<ref>[[Per Bak]] (1996). ''How Nature Works: The Science of Self-Organized Criticality'', Copernicus, New York, U.S.</ref>

[[File:Lorenz attractor yb.svg|thumb|right|200px|A plot of the [[Lorenz attractor]]]]

When one analyzes complex systems, sensitivity to initial conditions, for example, is not an issue as important as it is within chaos theory, in which it prevails. As stated by Colander,<ref>Colander, D. (2000). ''The Complexity Vision and the Teaching of Economics'', E. Elgar, Northampton, Massachusetts.</ref> the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioral patterns, whereas chaotic behavior, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions.<ref name="PC98" /> For recent examples in economics and business see Stoop et al.<ref>{{Cite journal |last1=Stoop |first1=Ruedi |last2=Orlando |first2=Giuseppe |last3=Bufalo |first3=Michele |last4=Della Rossa |first4=Fabio |date=2022-11-18 |title=Exploiting deterministic features in apparently stochastic data |journal=Scientific Reports |language=en |volume=12 |issue=1 |pages=19843 |bibcode=2022NatSR..1219843S |doi=10.1038/s41598-022-23212-x |issn=2045-2322 |pmc=9674651 |pmid=36400910}}</ref> who discussed [[Android (operating system)|Android]]'s market position, Orlando<ref>{{Cite journal |last=Orlando |first=Giuseppe |date=2022-06-01 |title=Simulating heterogeneous corporate dynamics via the Rulkov map |url=https://www.sciencedirect.com/science/article/pii/S0954349X22000121 |journal=Structural Change and Economic Dynamics |language=en |volume=61 |pages=32–42 |doi=10.1016/j.strueco.2022.02.003 |issn=0954-349X|url-access=subscription }}</ref> who explained the corporate dynamics in terms of mutual synchronization and chaos regularization of bursts in a group of chaotically bursting cells and Orlando et al.<ref>{{Cite journal |last1=Orlando |first1=Giuseppe |last2=Bufalo |first2=Michele |last3=Stoop |first3=Ruedi |date=2022-02-01 |title=Financial markets' deterministic aspects modeled by a low-dimensional equation |journal=Scientific Reports |language=en |volume=12 |issue=1 |pages=1693 |bibcode=2022NatSR..12.1693O |doi=10.1038/s41598-022-05765-z |issn=2045-2322 |pmc=8807815 |pmid=35105929}}</ref> who modelled financial data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity) with a low-dimensional deterministic model.

Therefore, the main difference between chaotic systems and complex systems is their history.<ref>Buchanan, M. (2000). ''Ubiquity : Why catastrophes happen'', three river press, New-York.</ref> Chaotic systems do not rely on their history as complex ones do. Chaotic behavior pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'.{{clarify|date=September 2011}} On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events, which physicist [[Murray Gell-Mann]] called "an accumulation of frozen accidents".<ref>Gell-Mann, M. (1995). What is Complexity?  Complexity 1/1, 16-19</ref> In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations.

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