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There are many definitions of complexity, therefore many natural and artificial 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, nervous systems, cells and living things, including human beings, as well as, modern energy or telecomunication infrastructures. Without doubts, the common property of complex systems is the difficulty of their formal modeling.

Beyond the fact that these things are all network 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.

Definition


The term complex system formally refers to a system of many parts which are coupled in a nonlinear fashion. Natural complex systems are modelled using the mathematical techniques of dynamical systems, which include differential equations, difference equations and maps. Because they are nonlinear, complex systems are more than the sum of their parts because a linear system is subject to the principle of superposition, and hence is literally the sum of its parts, while a nonlinear system is not. Put another way: a linear relationship is simply one whose graph is a straight line, so a linear connection between two things is one in which change on one side of the connection induces proportional change in the other. A nonlinear connection means that change on one side is not proportional to change on the other. When there are many non-linearities in a system (many components), behaviour can be as unpredictable as it is interesting. Complex systems research studies such behaviour.

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tablewhite (Tom Ablewhite) Wed, 16 Dec 2009 11:09:16 -0000
Financial Services Firms to Roll Out Complex Event Processing Systems from StreamBase http://snipurl.com/tpr1c [www_ebizq_net]
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This is good,really good! @CreatvEmergence connects dots between Improv & Complex Adaptive Systems http://bit.ly/8cQCLo (via @VenessaMiemis)
pawarm (Manoj Pawar) Wed, 16 Dec 2009 07:32:42 -0000
This is good,really good! @CreatvEmergence connects dots between Improv & Complex Adaptive Systems http://bit.ly/8cQCLo (via @VenessaMiemis)
@anjaligupta Take a look at Hidden Order by John Holland - good intro to complex adaptive systems. (via @tejus_sawjiani)
pawarm (Manoj Pawar) Wed, 16 Dec 2009 07:30:19 -0000
@anjaligupta Take a look at Hidden Order by John Holland - good intro to complex adaptive systems. (via @tejus_sawjiani)

 
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