Dynamic bifurcations: hysteresis, scaling laws and feedback control
N. Berglund
Prog. Theor. Phys. Suppl. 139:325-336 (2000)Proceedings of the 4th conference Let's face chaos through nonlinear dynamics, Maribor, Slovenia, June/July 1999
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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