This article describes complex system as field of science. For other meanings, see complex system.

Complex systems is a subfield of a systems science or systemics, which studies the common properties of systems considered complex in the nature, society and science. It is also called complex systems theory, complexity science, study of complex systems and/or sciences of complexity. The key problems of such systems are difficulties with their formal modeling and simulation. From such perspective, in different research contexts complex systems are defined on the base of their different attributes. At present, the consensus related to one universal definition of complex system does not exist yet.

Overview

The study of complex systems is bringing new vitality to many areas of science where a more typical reductionist strategy has fallen short. Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines including neurosciences, social sciences, meteorology, chemistry, physics, computer science, psychology, artificial life, evolutionary computation, economics, earthquake prediction, molecular biology and inquiries into the nature of living cells themselves.

In these endeavors, scientists often seek simple non-linear coupling rules which lead to complex phenomena (rather than describe - see above), but this need not be the case. Human societies (and probably human brains) are complex systems in which neither the components nor the couplings are simple. Nevertheless, they exhibit many of the hallmarks of complex systems.

Traditionally, engineering has striven to keep its systems linear, because that makes them simpler to build and to predict. However, many physical systems (for example lasers) are inherently "complex systems" in terms of the definition above, and engineering practice must now include elements of complex systems research.

Information theory applies well to the complex adaptive systems, CAS, through the concepts of object oriented design.

History

Complex Systems is a new approach to science that studies how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment.

The earliest precursor to modern complex systems theory can be found in the classical political economy of the Scottish Enlightenment, later developed by the Austrian school of economics, that order in market systems is spontaneous (or emergent) in that it is the result of human action, but not the execution of any human design ^{[1] [2]}.

Upon this and from the 19th to the early 20th century, the Austrian school developed the economic calculation problem along with the concept of dispersed knowledge, which were to fuel debates against the then-dominant Keynesian economics. This debate would notably lead economists, politicians and other parties to explore the question of computational complexity.

A pioneer in the field, and inspired by Karl Popper's and Warren Weaver's works, Nobel prize economist and philosopher Friedrich Hayek dedicated much of his work, from early to the late 20th century, to the study of complex phenomena ^[3], not constraining his work to human economies but to other fields such as psychology^[4], biology and cybernetics.

Further Steven Strogatz from Sync stated that "every decade or so, a grandiose theory comes along, bearing similar aspirations and often brandishing an ominous-sounding C-name. In the 1960s it was cybernetics. In the '70s it was catastrophe theory. Then came chaos theory in the '80s and complexity theory in the '90s."

Topics in the complex systems study

Complexity and modeling

One of Hayek's main contributions to early complexity theory is his distinction between the human capacity to predict the behaviour of simple systems and its capacity to predict the behaviour of complex systems through modeling. He believed that economics and the sciences of complex phenomena in general, which in his view included biology, psychology, and so on, could not be modeled after the sciences that deal with essentially simple phenomena like physics ^[5]. Hayek would notably explain that complex phenomena, through modeling, can only allow pattern predictions, compared with the precise predictions that can be made out of non-complex phenomena ^[6].

Complexity and chaos theory

Complexity theory takes its roots into Chaos theory, which 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 ^[7]. The point is that chaos remains deterministic. With perfect knowledge of the initial conditions and of the context of an action, the course of this action can be predicted in chaos theory. As argued by Prigogine ^[8], Complexity is non-deterministic, and gives no way whatsoever to predict the future. The emergence of complexity theory shows a domain between deterministic order and randomness which is complex ^[9]. This is referred as the 'edge of chaos'^[10].

When one analyses complex systems, sensitivity to initial conditions, for example, is not an issue as important as within the chaos theory in which it prevails. As stated by Colander ^[11], the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic set of relationships can generate some simple behavioural patterns, whereas chaotic behaviour, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions ^[12].

Therefore, the main difference between Chaotic systems and complex systems is their history ^[13]. Chaotic systems don’t rely on their history as complex ones do. Chaotic behaviour pushes a system in equilibrium into chaotic order, which means in other words, out of order. 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. In a sense chaotic systems can be regarded as a sub-set of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are in practice and over long but not everlasting time periods robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Meta-morphosis serves as perhaps more than a metaphor for such transformations.

Research centers, conferences, and journals

Institutes and research centers

• Santa Fe Institute
• Center for Complex Systems and Brain Sciences at Florida Atlantic University
• New England Complex Systems Institute
• COSI - Complexity in Social Science
• Center for the Study of Complex Systems at the University of Michigan
• Northwestern Institute on Complex Systems at Northwestern University
• Center for Complex Systems Research at the University of Illinois

Conferences

• NICO's Annual Complexity Conference
• NECSI's Sixth International Conference on Complex Systems (ICCS2006)
• IEEE International Conference on Engingineering of Complex Computer Systems (ICECCS2007)

Journals

• Advances in Complex Systems journal
• Chaos journal
• Complex Systems journal
• Complexity journal
• Complexity International journal
• Emergence: Complexity & Organization journal
• Interdisciplinary Description of Complex Systems journal

See also

References

Further reading

• L.A.N. Amarala and J.M. Ottino, Complex networks — augmenting the framework for the study of complex system, 2004.
• Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality, Copernicus, New York, USA.
• Buchanan, M.(2000). Ubiquity : Why catastrophes happen, three river press, New-York.
• Cilliers, P. (1998). Complexity and Postmodernism : Understanding Complex Systems, Routledge, London.
• Colander, D. (2000). The Complexity Vision and the Teaching of Economics, E. Elgar, Northampton, MA.
• Murray Gell-Mann, Let's Call It Plectics, 1995/96.
• Nigel Goldenfeld and Leo P. Kadanoff, Simple Lessons from Complexity, 1999
• A. Gogolin, A. Nersesyan and A. Tsvelik, Theory of strongly correlated systems , Cambridge University Press, 1999.
• Hayles, N. K. (1991). Chaos Bound : Orderly Disorder in Contemporary Literature and Science. Cornell University Press, Ithaca, NY.
• Kelly, K. (1995). Out of Control, Perseus Books Group.
• Prigogine, I. (1997). The End of Certainty, The Free Press, New York.
• Sorin Solomon and Eran Shir, Complexity; a science at 30, 2003.

External links

• "About Complex Systems" website, Northwestern Institute of Complex Systems.

•  • [ e] Global structure in Systems, Systems sciences and Systems scientists
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