Generic bifurcation of certain piecewise smooth vector fields

TL;DR

This paper investigates bifurcations in 2D piecewise-smooth dynamical systems, focusing on the unfolding of Resonant Fold-Saddle singularities within generic three-parameter families, and provides detailed bifurcation diagrams.

Contribution

It introduces a comprehensive analysis of the bifurcation structure of a specific class of non-smooth vector fields, particularly the Resonant Fold-Saddle singularity.

Findings

Bifurcation diagrams for the studied systems are explicitly characterized.

The unfolding of the Resonant Fold-Saddle singularity is systematically described.

Results enhance understanding of complex bifurcation scenarios in non-smooth dynamics.

Abstract

This paper presents results concerning bifurcations of 2D piecewise-smooth dynamical systems governed by vector fields. Generic three-parameter families of a class of Non-Smooth Vector Fields are studied and the bifurcation diagrams are exhibited. Our main results describe the unfolding of the so called Resonant $Fold-Saddle$ singularity.