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.
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Nils Berglund (1999) studied this question.
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