Control of Dynamic Hopf Bifurcations

Nils Berglund

doi:10.1088/0951-7715/13/1/311

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arXiv · chao-dyn/9904005

Control of Dynamic Hopf Bifurcations

Nils Berglund

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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 Lienard equation.

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Nils Berglund. 1999-03-31. Control of Dynamic Hopf Bifurcations. https://doi.org/10.1088/0951-7715%2F13%2F1%2F311

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