The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime
<|reference_start|>The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime: Li\'enard equations of the form $\ddot{x}+\epsilon f(x)\dot{x}+x=0$, with $f(x)$ an even function, are considered in the weakly nonlinear regime ($\epsilon\to 0$). 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 ${\mathcal O}(\epsilon^8)$ approximation for the amplitude of the van der Pol limit cycle is explicitly obtained.<|reference_end|>
@article{lopez2006the,
    title={The Limit Cycles of Lienard Equations in the Weakly Nonlinear Regime},
    author={Jose-Luis Lopez and Ricardo Lopez-Ruiz},
    journal={arXiv preprint arXiv:nlin/0605025},
    year={2006},
    archivePrefix={arXiv},
    eprint={nlin/0605025},
    primaryClass={nlin.AO cs.DM math.DS}
}