Quasi-Linear, parametrically excited van der Pol oscillator: Free and forced

The quasi-linear van der Pol oscillator subject to parametric excitation applied on its natural frequency is studied. The effect of this parametric excitation is analyzed, regular perturbation theory is used to determine the effect on the resulting frequency of oscillation; phase plane analysis and averaging method are both used to determine the effect on the amplitude of the solution. Having an external signal, the results help foreseeing the forcing strength required to suppress the natural frequency of the parametrically excited oscillator; or the one required by the parametrically excited oscillator to suppress the natural frequency of a second oscillator. This is a first approach to determine whether parametric excitation could be helpful for synchronization of oscillators.