On the birth of limit cycles for non-smooth dynamical systems

TL;DR

This paper develops a new approach combining Brower degree and regularization theories to detect limit cycles in non-smooth dynamical systems, providing novel insights into averaging methods.

Contribution

It introduces a variation of the averaging method tailored for non-smooth systems, linking it with non-smooth dynamical systems theory and demonstrating its effectiveness.

Findings

Existence of limit cycles in piecewise continuous systems established

New insights into averaging methods for non-smooth systems

Application example demonstrating the approach

Abstract

The main objective of this work is to develop, via Brower degree theory and regularization theory, a variation of the classical averaging method for detecting limit cycles of certain piecewise continuous dynamical systems. In fact, overall results are presented to ensure the existence of limit cycles of such systems. These results may represent new insights in averaging, in particular its relation with non smooth dynamical systems theory. An application is presented in careful detail.