# On Typical Homoclinic-Like Loops in 3D Filippov Systems

## TL;DR

This paper investigates a unique homoclinic-like loop in 3D Filippov systems, demonstrating its robustness, analyzing its basin of attraction, and revealing phenomena absent in smooth systems.

## Contribution

It introduces the analysis of a homoclinic-like loop in Filippov systems, showing its robustness and bifurcation structure, with novel techniques distinct from smooth system analysis.

## Key findings

- The homoclinic-like loop is robust in one-parameter families.
- The basin of attraction for the loop is computed.
- The phenomenon has no counterpart in smooth 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.