Dynamic bifurcations: hysteresis, scaling laws and feedback control

Details Dynamic bifurcations: hysteresis, scaling laws and feedback control Dynamic bifurcations: hysteresis, scaling laws and feedback control

1999-12-06

arxiv.org/abs/chao-dyn/9912008v1

Prog. Theor. Phys. Suppl. 139:325-336 (2000)

Nonlinear Sciences

Chaotic Dynamics

12 pages, 2 PS figures, LaTeX2e, proceedings of summer school (Maribor 1999)

Scientific paper

10.1143/PTPS.139.325

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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