99-89 N. Berglund

Control of Dynamic Hopf Bifurcations (127K, LaTeX 2e with 4 PS Figures) Mar 30, 99

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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 Li\'enard equation.

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