Dynamical Systems Theory, Bifurcation Analysis
Bifurcation theory refers to the study of qualitative changes to the state of a system as a parameter is varied. It can be applied to steady state systems, or to dynamical systems and can be understood best at the level of a mathematical model, although recent techniques allow the method to be applied to experiments with feedback control. Typically the theory is applied to a continuous model, but can also be used in discrete models and mathematics, difference equations. There are dedicated numerical implementations of bifurcation theory using path-following, or numerical continuation. There is a distinction between a local bifurcation, which can be understood in terms of a change to the number or stability of simple steady states, and a global bifurcation, which cannot. Often global bifurcations cause catastrophic changes to the attractorof the system. Typical local examples...
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