Bifurcation theory

Study of sudden qualitative behavior changes caused by small parameter changes / From Wikipedia, the free encyclopedia

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Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.[1] Bifurcations occur in both continuous systems (described by ordinary, delay or partial differential equations) and discrete systems (described by maps).

Phase portrait showing saddle-node bifurcation

The name "bifurcation" was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior.[2]

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