On the number of limit cycles of polynomial Lienard systems

TL;DR

This paper introduces a new method to estimate the maximum number of limit cycles in polynomial Lienard systems, significantly improving previous bounds and advancing understanding of oscillatory behavior in these models.

Contribution

A novel approach for lower bounds on the number of limit cycles in polynomial Lienard systems of arbitrary degree.

Findings

New lower bounds for the number of limit cycles

Improved estimations over existing results

Applicable to polynomial Lienard systems of any degree

Abstract

Lienard systems are very important mathematical models describing oscillatory processes arising in applied sciences. In this paper, we study polynomial Lienard systems of arbitrary degree on the plane, and develop a new method to obtain a lower bound of the maximal number of limit cycles. Using the method and basing on some known results for lower degree we obtain new estimations of the number of limit cycles in the systems which greatly improve existing results.