Planar quartic–quadratic fold–fold singularity of Filippov systems and its bifurcation

Abstract

In this paper it is exhibited the bifurcation scenario concerning a typical singularity of planar piecewise smooth vector fields in two zones. This singularity is characterized by a quadratic contact of one vector field and a quartic contact of another vector field at the same point of the switching manifold. By means of a three parameter perturbation, we observe the presence of bifurcations like: Hopf Bifurcation, Sliding Hopf Bifurcation, the birth and annihilation of chaotic scenarios, among others. The two and three dimensional bifurcation diagrams are included.