Universitat Politècnica de Catalunya, Barcelona
Sliding bifurcations after Sotomayor–Teixeira regularization: an application of singular perturbation theory to Filippov systems.
In this talk we do a detailed study, using geometric singular perturbation theory and matching asymptotic expansions, of the Sotomayor–Teixeira regularization of a Filippov system near a visible tangency. The main goal is to understand how global bifurcations involving sliding, which are typical for non-smooth systems, evolve to classical well-known bifurcations when the system is regularized.
We apply the local study to understand some global bifurcations of periodic orbits and homoclinic orbits. We take a one-parameter family of Filippov vector fields in the plane having a grazing-sliding bifurcation and we analyze the behavior in the corresponding regularized system. We relate the grazing sliding bifurcation of a repelling periodic orbit with the classical saddle node bifurcation. We also study a grazing homoclinic bifurcation.
This is joint work with Carles Bonet from the Universitat Politècnica de Catalunya.