Control of Dynamic Hopf Bifurcations
chao-dyn
2007-05-23 v1 Optimization and Control
Chaotic Dynamics
Abstract
The slow passage through a Hopf bifurcation leads to the delayed appearance of large amplitude oscillations. We construct a smooth scalar feedback control which suppresses the delay and causes the system to follow a stable equilibrium branch. This feature can be used to detect in time the loss of stability of an ageing device. As a by-product, we obtain results on the slow passage through a bifurcation with double zero eigenvalue, described by a singularly perturbed cubic Lienard equation.
Cite
@article{arxiv.chao-dyn/9904005,
title = {Control of Dynamic Hopf Bifurcations},
author = {Nils Berglund},
journal= {arXiv preprint arXiv:chao-dyn/9904005},
year = {2007}
}
Comments
25 pages, 4 figures