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Complexity and chaos

Chaos is defined as a state of utter confusion or disorder, a total lack of organisation or order. This is different than complexity. Learn more here.
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Chaos is defined as a state of utter confusion or disorder, a total lack of organisation or order. This is different than complexity, in which chaos is often confused. Our universe is complex, but not chaotic, says Richard Pascal in Surfing the Edge of Chaos. Chaos theory is based on the principles that what appears chaotic inherently contains order. Small changes cause varied outcomes due to iteration, also known as the butterfly effect. And the equations associated with prediction are dynamic rather than linear. Complex and chaotic systems are both examples of nonlinear dynamical systems. A linear system is characterised by the satisfaction of the Superposition principle.
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The Superposition principle says that if A and B are both solutions for some system, ways in which the system could evolve. Then so is their sum, A plus B. This implies that a linear system can be decomposed into its parts, and each part solves separately to construct the full solution. For nonlinear systems, this is not possible, because of the appearance of nonlinear terms, functions of the variables, such as Sin(x), x3, and xy. In this sense then, the whole here is more than the sum of its parts. Given this, a nonlinear system is one for which inputs are not proportional to outputs.
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A small (large) change in some variable, or family of variables, will not necessarily result in a small (large) change in the system. This kind of behaviour is well known to those involved in Intervention Research. Large interventions in some variable do not necessarily have a large effect on some outcome variable of interest. Likewise, a small intervention can have a large unexpected outcomes. Chaos is the generation of complicated, aperiodic, seemingly random behaviour from the iteration of a simple rule. This complicatedness is not complex in the sense of a complex system science, but rather it is chaotic in a very precise mathematical sense. Complexity is the generation of rich, collective, dynamic behaviour from simple interactions between large numbers of subunits.
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Chaotic systems are not necessarily complex. And complex systems are not necessarily chaotic, although they can be, for some values of the variables or control parameter.

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Chaos is defined as a state of utter confusion or disorder, a total lack of organisation or order. This is different than complexity, with which chaos is often confused.

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