Bifurcation Curves of Limit Cycles in some Lienard Systems

2002/05/14 by Ricardo López‐Ruiz, Ricardo Lopez-Ruiz, Lopez-Ruiz, Ricardo +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #Quantum chaos and dynamical systems #math.DS #nlin.PS

paper · pdf · doi:10.48550/arxiv.nlin/0205028

25 pages, 0 figures. Published in Int. Journal of Bifurcation and Chaos, vol. 10, 971-980 (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 continous function, are considered. The bifurcation curves of limit cycles are calculated exactly in the weak (ε→ 0) and in the strongly (ε→∞) nonlinear regime in some examples. The number of limit cycles does not increase when ε increases from zero to infinity in all the cases analyzed.

Related

• The Limit Cycles of Lienard Equations in the Strongly Non-Linear Regime
• On the Existence of Exactly N Limit Cycles in Lienard Systems
• Limit cycles of a Liénard system with symmetry allowing for discontinuity
• The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime
• On the determination of exact number of limit cycles in Lienard Systems