Quenching phenomena in synchronized Van de Pol systems

Quenching of sinusoidally driven Van der Pol systems is considered and conditions developed under which harmonic synchronous quenching occurs. For this, a multiple time expansion is used to solve the Van der Pol equation with the sinusoidal forcing term. By controlling the expansion in terms of a small parameter and equating terms of like order in the parameter, the solutions of asynchronous and synchronous state are obtained. From these solutions the conditions for harmonic synchronous quenching are developed and a plot given to show the quenching region