The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime

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Liénard equations of the form $\ddot{x}+εf(x)\dot{x}+x=0$, with $f(x)$ an even function, are considered in the weakly nonlinear regime ($ε\to 0$). 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 ${\mathcal O}(ε^8)$ approximation for the amplitude of the van der Pol limit cycle is explicitly obtained.
17 text-pages, 1 table, 6 figures

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Adaptation and Self-Organizing Systems, Discrete Mathematics, Dynamical Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/113031

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0605025
 http://arxiv.org/abs/nlin/0605025

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arXiv