Van der Pol's oscillator under the parametric and forced excitations

Abstract

Van der Pol's oscillator under parametric and forced excitations is studied. The case where the system contains a small parameter being quasilinear and the general case (without assumption on the smallness of nonlinear terms and perturbations) are studied. In the first case, equations of the first approximation are obtained by means of the Krylov-Bogoliubov-Mitropolskii technique, their averaging is performed, frequency amplitude and resonance curves are studied, on the stability of the given system is considered. In the second case, the possibility of chaotic behavior in a deterministic system of oscillator type is shown.