Complex system

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There are many definitions of complexity, therefore many natural, artificial and abstract objects or networks can be considered to be complex systems, and their study (complexity science) is highly interdisciplinary. Examples of complex systems include ant-hills, ants themselves, human economies, climate, nervous systems, cells and living things, including human beings, as well as modern energy or telecommunication infrastructures.

Beyond the fact that these things are all networks of some kind, and that they are complex, it may appear that they have little in common, hence that the term "complex system" is vacuous. However, all complex systems are held to have behavioural and structural features in common, which at least to some degree unites them as phenomena. They are also united theoretically, because all these systems may, in principle, be modelled with varying degrees of success by a certain kind of mathematics. It is therefore possible to state clearly what it is that these systems are supposed to have in common with each other, in relatively formal terms.

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[edit] Definition

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.

[edit] 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 physicist Henri Poincaré. Chaos is sometimes viewed as extremely complicated information, rather than as an absence of order (Hayles, 1991). 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 (2002), 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 (Cilliers, 1998). This is referred as the 'edge of chaos' (Bak, 1996).

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 (2000), 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 (Cilliers, 1998).

Therefore, the main difference between Chaotic systems and complex systems is their history (Buchanan, 2000). 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.

[edit] Applications of complex systems theory

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, heart cell synchronisation, immune systems, reaction-diffusion systems, molecular biology, epilepsy 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.

[edit] Socio-cognitive complexity

Socio-cognitive systems are complex from their nature. They include humans, organizations and are intelligence-based systems. The study of socio-cognitive complexity is the new domain in systemics and has to cope with a meta-complexity on higher levels in the hierarchy of abstract systems.[citation needed]

[edit] Features of complex systems in nature

[edit] Relationships are non-linear

In practical terms, this means a small perturbation may cause a large effect (see butterfly effect), a proportional effect, or even no effect at all. In linear systems, effect is always directly proportional to cause. See nonlinearity.

[edit] Relationships contain feedback loops

Both negative (damping) and positive (amplifying) feedback are often found in complex systems. The effects of an element's behaviour are fed back to in such a way that the element itself is altered.

[edit] Complex systems are open

Complex systems in nature are usually open systems — that is, they exist in a thermodynamic gradient and dissipate energy. In other words, complex systems are usually far from energetic equilibrium: but despite this flux, there may be pattern stability. See synergetics.

[edit] Complex systems have a memory

The history of a complex system may be important. Because complex systems are dynamical systems they change over time, and prior states may have an influence on present states. More formally, complex systems often exhibit hysteresis.

[edit] Complex systems may be nested

The components of a complex system may themselves be complex systems. For example, an economy is made up of organisations, which are made up of people, which are made up of cells - all of which are complex systems.

[edit] Boundaries are difficult to determine

It can be difficult to determine the boundaries of a complex system. The decision is ultimately made by the observer.

[edit] Dynamic network of multiplicity

As well as coupling rules, the dynamic network of a complex system is important. Small-world or scale-free networks which have many local interactions and a smaller number of inter-area connections are often employed. Natural complex systems often exhibit such topologies. In the human cortex for example, we see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions.

[edit] May produce emergent phenomena

Complex systems may exhibit behaviors that are emergent, which is to say that while the results may be deterministic, they may have properties that can only be studied at a higher level. For example, the termites in a mound have physiology, biochemistry and biological development that are at one level of analysis, but their social behavior and mound building is a property that emerges from the collection of termites and needs to be analysed at a different level.

[edit] References

  • Bak, P. (1996). How Nature Works: The Science of Self-Organized Ccriticality, 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.
  • Hayles, N. K. (1991). Chaos Bound : Orderly Disorder in Contemporary Literature and Science. Cornell University Press, Ithaca, NY.
  • Prigogine, I. (1997). The End of Certainty, The Free Press, New York.

[edit] Quotes

  • From Sync by Steven Strogatz: "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."

Various informal descriptions of complex systems have been put forward, and these may give some insight into their properties. A special edition of Science about complex systems Science Vol. 284. No. 5411 (1999). highlighted several of these:

  • A complex system is a highly structured system, which shows structure with variations (Goldenfeld and Kadanoff)
  • A complex system is one whose evolution is very sensitive to initial conditions or to small perturbations, one in which the number of independent interacting components is large, or one in which there are multiple pathways by which the system can evolve (Whitesides and Ismagilov)
  • A complex system is one that by design or function or both is difficult to understand and verify (Weng, Bhalla and Iyengar)
  • A complex system is one in which there are multiple interactions between many different components (D. Rind)
  • Complex systems are systems in process that constantly evolve and unfold over time (W. Brian Arthur).

[edit] See also

[edit] External links

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 London School of Economics Complexity Research Programme

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