On the limit cycle of a generalized van der Pol equation (Q1261598)

The limit cycle of a generalized van der Pol equation of the form \(\ddot u+u=\varepsilon(1-u^{2n})\dot u\) is investigated, where \(\varepsilon\) is small and \(n\) is any positive integer. Using the derivative expansion version of the method of multiple scales, a perturbation solution is derived for the displacement to first order in \(\varepsilon\) and for the phase to second order in \(\varepsilon\). The perturbation solution is compared with numerical solutions obtained using the IMSL routines DIVPRK and DIVPAG. The first-order perturbation solution becomes less accurate as \(n\) increases.