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.


The Catalan Mathematical Society invites participants to this first congress of a biannual series focusing on current research topics across several areas of Mathematics.

Plenary talks and thematic sessions have been selected by the Scientific Committee of the SCM. Special thanks are due to the organisers of the thematic sessions and to the local mathematical community as a whole for their support to this congress.



Societat Catalana de Matemàtiques
Institut d'Estudis Catalans
Carrer del Carme, 47
08001 Barcelona

Phone: +34 933 248 583

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