Van der Pol oscillator under parametric and forced excitations

Abstract

We study a van der Pol oscillator under parametric and forced excitations. The case where a system contains a small parameter and is quasilinear and the general case (without the assumption of the smallness of nonlinear terms and perturbations) are studied. In the first case, equations of the first approximation are obtained by the Krylov-Bogolyubov-Mitropol’skii technique, their averaging is performed, frequency-amplitude and resonance curves are studied, and 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.