Abstract

Nonautonomous bifurcation theory studies the change of attractors of nonautonomous systems which are introduced here with the process formalism as well as the skew product formalism.
Two principles underlie the talk: a total stability theorem ensures the existence of nearby attractors of perturbed systems and these perturbed attractors depend continuously on a parameter if and only if the attraction is uniform w.r.t. parameter, i.e. the attractors are equiattracting.
These will be applied to explicit systems to clarify the meaning of continuous and abrupt transitions of attractors in contrast to bifurcations, i.e. splitting of minimal invariant subsets into others within the attractor. Several examples are treated, including a nonautonomous pitchfork bifurcation.
The talk is based on the paper
P.E. Kloeden and S. Siegmund, Bifurcation and continuous transition of attractors in autonomous and nonautonomous systems, Inter. J. Bifurcation & Chaos, 15 (2005), 743--762.