Dynamic bifurcations: hysteresis, scaling laws and feedback control

Nils 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.

 

Journal Homepage Published article: 10.1143/PTPS.139.325

PDF file (212 Kb) hal-00130575 arXiv/chao-dyn/9912008