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Approximating the Amplitude and Form of Limit Cycles in the Weakly Nonlinear Regime of Lienard Systems

Jose-Luis Lopez·Ricardo Lopez-Ruiz
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Abstract

Liénard equations, $\ddot{x}+εf(x)\dot{x}+x=0$, with $f(x)$ an even continuous function are considered. In the weakly nonlinear regime ($ε\to 0$), the number and an order zero in $ε$ approximation of the amplitude of limit cycles present in this type of systems can be obtained by applying a methodology recently proposed by the authors [López-Ruiz R, López JL. Bifurcation curves of limit cycles in some Liénard systems. Int J Bifurcat Chaos 2000; 10:971-980]. In the present work, that method is carried forward to higher orders in $ε$ and is embedded in a general recursive algorithm capable to approximate the form of the limit cycles and to correct their amplitudes as an expansion in powers of $ε$. Several examples showing the application of this scheme are given.

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Jose-Luis Lopez, Ricardo Lopez-Ruiz. 2006-03-31. Approximating the Amplitude and Form of Limit Cycles in the Weakly Nonlinear Regime of Lienard Systems. https://doi.org/10.1016/j.chaos.2006.04.031

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