The Generic Unfolding of a Codimension-Two Connection to a Two-Fold Singularity of Planar Filippov Systems

Generic bifurcation theory was classically well developed for smooth differential systems, establishing results for k-parameter families of planar vector
elds. In the present study we focus on a qualitative analysis of 2-parameter families, Za,ß of planar Filippov systems assuming that Zo;o presents a codimension- two minimal set. Such object, named elementary simple two-fold cycle, is characterized by a regular trajectory connecting a visible two-fold singularity to itself, for which the second derivative of the rst return map is nonvanishing. We analyzed the codimension-two scenario through the exhibition of its bifurcation diagram.