Dynamic bifurcations: hysteresis, scaling laws and feedback control
chao-dyn
2009-10-31 v1 Chaotic Dynamics
Abstract
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.
Cite
@article{arxiv.chao-dyn/9912008,
title = {Dynamic bifurcations: hysteresis, scaling laws and feedback control},
author = {N. Berglund},
journal= {arXiv preprint arXiv:chao-dyn/9912008},
year = {2009}
}
Comments
12 pages, 2 PS figures, LaTeX2e, proceedings of summer school (Maribor 1999)