2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/113031Liénard 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 figuresAdaptation and Self-Organizing SystemsDiscrete MathematicsDynamical Systemstext