On Typical Homoclinic-Like Loops in 3D Filippov Systems

Abstract

In this work a homoclinic-like loop of a piecewise smooth vector field passing through a typical singularity is analyzed. We have shown that such a loop is robust in one-parameter families of Filippov systems. The basin of attraction of this connection is computed as well as its bifurcation diagram. It is worthwhile to mention that this phenomenon has no counterpart in the smooth world and the techniques used in this analysis differ from the usual ones.