Control of Dynamic Hopf Bifurcations

Nils Berglund
Nonlinearity 13, 225-248 (2000)

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 Liénard equation.

Key words and phrases: Hopf bifurcation, nonlinear control theory, singular perturbations, dynamic bifurcations, codimension four unfolding, Liénard equation.

1991 Mathematics Subject Classification: 34E15, 58F14, 93D15.

Keywords and phrases: Hopf bifurcation, nonlinear control theory, singular perturbations, dynamic bifurcations, codimension four unfolding, Liénard equation.

 

Journal Homepage Published article: 10.1088/0951-7715/13/1/311 MR1734631 Zbl1016.34039

PDF file (452 Kb) hal-00130547 arXiv/chao-dyn/9904005