  In this paper, we are concerned about the qualitative behavior of planar
Filippov systems around some typical invariant sets, namely, polycycles. In the
smooth context, a polycycle is a simple closed curve composed by a collection
of singularities and regular orbits, inducing a first return map. Here, this
concept is extended to Filippov systems by allowing typical Filippov
singularities lying on the switching manifold. Our main goal consists in
developing a method to investigate the unfolding of polycycles in Filippov
systems. In addition, we apply this method to describe bifurcation diagrams of
Filippov systems around certain polycycles.
