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Article Dans Une Revue Progress in theoretical physics suppl. Année : 2000

Dynamic bifurcations: hysteresis, scaling laws and feedback control

Nils Berglund

Résumé

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.

Dates et versions

hal-00130575 , version 1 (12-02-2007)

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Nils Berglund. Dynamic bifurcations: hysteresis, scaling laws and feedback control. Progress in theoretical physics suppl., 2000, 139, pp.325-336. ⟨10.1143/PTPS.139.325⟩. ⟨hal-00130575⟩

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