The Limit Cycles of Lienard Equations in the Strongly Non-Linear Regime

2002/05/14 by José L. López, Jose-Luis Lopez, Lopez, Jose-Luis +3
Mathematics · Medicine · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems #math.DS #nlin.CD #nlin.PS

paper · pdf · doi:10.48550/arxiv.nlin/0205027

22 pages, 0 figures. Published in Chaos, Solitons and Fractals, vol. 11, 747-756 (2001)

arxiv created 2002/05/14 · openalex publication_date 2002/05/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Lienard systems of the form x+εf(x)x+x=0, with f(x) an even function, are studied in the strongly nonlinear regime (ε→∞). A method for obtaining the number, amplitude and loci of the limit cycles of these equations is derived. The accuracy of this method is checked in several examples. Lins-Melo-Pugh conjecture for the polynomial case is true in this regime.

Related

• The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime
• On the determination of exact number of limit cycles in Lienard Systems
• Bifurcation Curves of Limit Cycles in some Lienard Systems
• On the number of limit cycles of polynomial Lienard systems
• A note on existence and uniqueness of limit cycles for Liénard systems