Control of Dynamic Bifurcations

We consider diierential equations _ x = 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 suucient. For Hopf bifurcations, we have to construct a more elaborate control creating a suitable bifurcation with double zero eigenvalue.