# Bifurcation Diagrams of Global Connections in Filippov Systems

## TL;DR

This paper extends the concept of polycycles to Filippov systems with singularities on switching manifolds, developing a method to analyze their bifurcations and unfolding behavior.

## Contribution

It introduces a novel approach for studying bifurcations of polycycles in Filippov systems, including singularities on switching manifolds.

## Key findings

- Developed a method to analyze unfolding of polycycles in Filippov systems.
- Described bifurcation diagrams around specific polycycles.
- Extended the concept of polycycles to nonsmooth systems with singularities.

## Abstract

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.