Control of Dynamic Hopf Bifurcations

Details Control of Dynamic Hopf Bifurcations Control of Dynamic Hopf Bifurcations

1999-03-31

arxiv.org/abs/chao-dyn/9904005v1

Nonlinearity 13:225-248 (2000)

Mathematics

Optimization and Control

25 pages, 4 figures

Scientific paper

10.1088/0951-7715/13/1/311

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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