Control of Dynamic Hopf Bifurcations
- Berglund, Nils
2010 Mathematics Subject Classification
- 34E15 58F14 93D15
- Hopf bifurcation, nonlinear control theory, singular perturbations, dynamic bifurcations, codimension four unfolding, Liénard equation
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.
- Nonlinearity 13, 225-248 (2000)