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Frequency Locking in a Forced Mathieu-van der Pol System

In this paper we investigate the dynamics of a Mathieuvan der Pol equation, which is forced both parametrically and nonparametrically. It is shown that the steady state response can consist of either 1:1 frequency locking, or 2:1 subharmonic locking, or quasiperiodic motion. The system displays hysteresis when the forcing frequency is slowly varied. We use perturbations to obtain a slow flow, which is then studied using the bifurcation software package AUTO. This study was motivated by an application to a MEMS device.