Limit cycles of a class of piecewise smooth Li\'enard systems

TL;DR

This paper investigates the bifurcation of limit cycles in specific piecewise polynomial Li'enard systems using Melnikov function theory to determine the maximum number of limit cycles.

Contribution

It develops a Melnikov function approach to analyze limit cycle bifurcations in two new classes of piecewise polynomial Li'enard systems, providing maximum limit cycle counts.

Findings

Maximum number of limit cycles for the systems is established.

Melnikov function theory is effectively applied to piecewise polynomial systems.

Results contribute to understanding bifurcations in nonsmooth dynamical systems.

Abstract

In this paper, we study the problem of limit cycle bifurcation in two piecewise polynomial systems of Li\'enard type with multiple parameters. Based on the developed Melnikov function theory, we obtain the maximum number of limit cycles of these two systems.