Control of Dynamic Bifurcations

Nils Berglund and Klaus R. Schneider
Stability and Stabilization of Nonlinear Systems (Ghent, 1999), 75-93 (Springer-Verlag, Berlin, 1999)

We consider differential equations dx/dt = f(x, ) where the parameter = t moves slowly through a bifurcation point of f. Such a dynamic bifurcation is often accompanied by a possibly dangerous jump transition. We construct smooth scalar feedback controls which avoid these jumps. For transcritical and pitchfork bifurcations, a small constant additive control is usually sufficient. For Hopf bifurcations, we have to construct a more elaborate control creating a suitable bifurcation with double zero eigenvalue.

Key words and phrases: Bifurcation theory, nonlinear control theory, singular perturbations, dynamic bifurcations, unfolding.

1991 Mathematics Subject Classification: 34E15, 58F14, 93D15.

 

Journal Homepage Published article: 10.1007/1-84628-577-1_4 MR1714584 Zbl0932.93037

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