On Degenerate Cycles in Planar Filippov Systems

The main objective of this paper is to study bifurcations of a vector field in a neighborhood of a cycle having a homoclinic-like connection at a saddle-regular point. In order to perform such a study it is necessary to analyze how the cycle can be broken, in this way the approach is to look separately at local bifurcations and at the structure of the first return map defined near the cycle.