Nonlinearity

:This article describes the use of the term nonlinearity in mathematics. For other meanings, see nonlinearity (other uses).

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In mathematics, nonlinear systems represented systems whose behavior is not expressible as a linear function of its descriptors; that is, such systems are not linear.

Related Topics:
Mathematic - Linear

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As such, the behavior of nonlinear systems is not subject to the principle of superposition.

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An example of superposition is the following:

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:f(x)+f(y) = f(x+y)

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The combination of the function f acting on x and acting on y is identical to it acting on the sum of x and y.

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In a sense, linearity means that the system is the sum of its parts.

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This allows us to make certain mathematical assumptions and approximations.

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Being linear also means the system's solutions are easier to compute.

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In nonlinear systems these assumptions cannot be made, the system is more than the sum of its parts, which causes nonlinear systems to be extremely hard (or impossible) to model.

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As such their behavior over a given variable (for example, time) is extremely difficult to predict.

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In nonlinear systems one encounters such phenomena as chaos effects, strange attractors, and freak waves. Whilst some nonlinear systems and equations of general interest have been extensively studied, the vast majority are poorly understood if at all.

Related Topics:
Chaos - Strange attractor - Freak waves

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Nonlinear systems are probably easiest understood as "everything except the relatively few systems which prove to be linear".

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