Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2006-05-10
Nonlinear Sciences
Adaptation and Self-Organizing Systems
17 text-pages, 1 table, 6 figures
Scientific paper
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.
Lopez Jose-Luis
López-Ruiz Ricardo
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