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Encyclopedia > Nonlinear

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  • http://www.enm.bris.ac.uk/research/nonlinear/faq-Contents.html

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Nonlinearity - Wikipedia, the free encyclopedia (720 words)
Since nonlinear systems are not equal to the sum of their parts, they are often difficult (or impossible) to model, and their behavior with respect to a given variable (for example, time) is extremely difficult to predict.
Nonlinear equations and functions are of interest to physicists and mathematicians because most physical systems are inherently nonlinear in nature.
For nonlinear equations the solutions to the equations do not in general form a vector space and cannot (in general) be superposed (added together) to produce new solutions.
Nonlinearity - definition of Nonlinearity in Encyclopedia (403 words)
A nonlinear equation, is an equation that do not satisfy the conditions for a linear equation.
Equations involving maps includes linear equations, and nonlinear equations as well as nonlinear systems (the last is a misdenomer steaming from matrix equations 'systems', a nonlinear equation can be a scalar valued or matrix valued equation).
Today there are several tools for analyzing nonlinear equations, to mention a few: Implicit function theorem, Contraction mapping principle and the theory of bifurcations.
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