Dynamic Bifurcations: Hysteresis, Scaling Laws and Feedback Control
Abstract
We review some properties of dynamical systems with slowly varyingparameters, 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.
- Publication:
-
Progress of Theoretical Physics Supplement
- Pub Date:
- 2000
- DOI:
- 10.1143/PTPS.139.325
- arXiv:
- arXiv:chao-dyn/9912008
- Bibcode:
- 2000PThPS.139..325B
- Keywords:
-
- Nonlinear Sciences - Chaotic Dynamics
- E-Print:
- 12 pages, 2 PS figures, LaTeX2e, proceedings of summer school (Maribor 1999)