On the number of limit cycles of polynomial Lienard systems

2011/09/29 by Maoan Han, Han, Maoan, Valery G. Romanovski +1
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1109.6470

openalex publication_date 2011/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• The general Liénard polynomial system
• On the Existence of Exactly N Limit Cycles in Lienard Systems
• A note on existence and uniqueness of limit cycles for Liénard systems
• The number of medium amplitude limit cycles of some generalized Liénard systems
• On the determination of exact number of limit cycles in Lienard Systems