Oberseminar "Dynamische Systeme und Kontrolltheorie" - Dr. Victor Avrutin

The key question of the bifurcation theory - what may happen if the parameters of a dynamical system are varied - is both challenging from the theoretical point of view and important for a broad range of real-world application. However, for historical reasons, the classical bifurcation theory has been developed mainly for smooth models, while many models originating from such fields as mechanics, electronics, economics, etc., are necessarily piecewise-smooth. In such systems, the state space is subdivided into partitions associated with different dynamics and separated from each other by so-calledswitching manifolds. As a consequence, piecewise-smooth systems show several phenomena which can not occur in smooth systems, as they are caused by interactions between invariant sets and switching manifolds. Moreover, many fundamental results rigorously proven for smooth systems are no longer valid for piecewise-smooth ones.

I this talk, we recall first some basic concepts from the classical bifurcation theory for smooth systems, and then we focus on the question which additional effects may occur if the model under consideration is piecewise-smooth.