The term complex system formally refers to a system of many parts which are coupled in a nonlinear fashion. Such a system may be discrete (such as a cellular automata system or set of difference equations), or it may be continuous as in a system of differential equations. 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.

From Wikipedia http://en.wikipedia.org/wiki/Complex_systems

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