Effect of parametric excitation on the quasi-linear van der Pol oscillator

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 to determine the effect on the amplitude and frequency of the solution. Considering an external signal, the results of these analyses are used to determine upper and lower bounds of the forcing strength required to suppress the natural frequency of the parametrically excited oscillator, as well as in the case when the parametrically excited oscillator forces a second oscillator.