WIAS Preprint No. 479, (1999)

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.

Appeared in

  • Nonlinearity 13, 225-248 (2000)

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