On the Existence of Exactly $N$ Limit Cycles in Lienard Systems

TL;DR

This paper proves a theorem determining the exact number of limit cycles around a critical point in Lienard systems and proposes an algorithm to identify this number even with incomplete data.

Contribution

It introduces a new theorem for exactly counting limit cycles in Lienard systems and an algorithm applicable with incomplete system data.

Findings

Proved a theorem on the existence of exactly N limit cycles in Lienard systems.

Developed an algorithm to determine the number of limit cycles with incomplete data.

Applicable to systems where data is partially known or uncertain.

Abstract

A theorem on the existence of exactly $N$ limit cycles around a critical point for the Lienard system $\ddot{x}+f(x) \dot{x}+g(x) =0$ is proved. An alogrithm on the determination of a desired number of limit cycles for this system has been considered which might become relevant for a Lienard system with incomplete data.