| Abstract: | Abstract The properties of the limit cycle of a generalised van der Pol equation of the form ü + u = ε (1—u2n)u, where ε is small and n is any positive integer, are investigated by applying a time transformation perturbation method due to Burton. It is found that as n increases the amplitude of the limit cycle oscillation decreases and its period increases. The time transformation solution is compared with the solution derived using the method of multiple scales and with a numerical solution. It is found that, to first order in ε, the time transformation solution for the limit cycle agrees better with the numerical solution than the multiple scales solution. Both perturbation solutions give the same result for the period of the limit cycle to second order in ε. The accuracy of the time transformation solution decreases as n increases. |
