The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime

2006/05/10 by Jose-Luis Lopez, Lopez, Jose-Luis, Ricardo Lopez-Ruiz +1
Computer Science · Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Discrete Mathematics (cs.DM) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #cs.DM #math.DS #nlin.AO

paper · pdf · doi:10.48550/arxiv.nlin/0605025

17 text-pages, 1 table, 6 figures

arxiv created 2006/05/10 · arxiv updated 2009/12/01

Abstract

Liénard equations of the form x+εf(x)x+x=0, with f(x) an even function, are considered in the weakly nonlinear regime (ε→ 0). A perturbative algorithm for obtaining the number, amplitude and shape of the limit cycles of these systems is given. The validity of this algorithm is shown and several examples illustrating its application are given. In particular, an \mathcal O(ε⁸) approximation for the amplitude of the van der Pol limit cycle is explicitly obtained.

Related

• The Limit Cycles of Lienard Equations in the Strongly Non-Linear Regime
• On the determination of exact number of limit cycles in Lienard Systems
• Bifurcation Curves of Limit Cycles in some Lienard Systems
• A note on existence and uniqueness of limit cycles for Liénard systems
• On the Existence of Exactly N Limit Cycles in Lienard Systems