Dynamic bifurcations: hysteresis, scaling laws and feedback control

N. Berglund

doi:10.1143/ptps.139.325

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arXiv · chao-dyn/9912008

Dynamic bifurcations: hysteresis, scaling laws and feedback control

N. Berglund

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Abstract

We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area scales in a nontrivial way with the adiabatic parameter. Hopf bifurcations lead to the delayed appearance of oscillations. Feedback control theory motivates the study of a bifurcation with double zero eigenvalue, in which this delay is suppressed.

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N. Berglund. 1999-12-06. Dynamic bifurcations: hysteresis, scaling laws and feedback control. https://doi.org/10.1143/ptps.139.325

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