Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family, 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 behaviour.
See:
MIT Video - Bifurcation theory
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