Chaos and Control in a Van Der Pol-Duffing System

This paper studies the chaotic dynamics of a VanderPol-Duffing system.Using the direct perturbation method,the authors construct the general solution of the system.Through the general solution the authors obtain the Melnikov criterion predicting onset of chaos.In the unperturbed situations,the phase portraits and corresponding Poincare sections show that the system can step into chaos via a period-doubling route through changing the intensities of damping and external forcing.The chaos of the system can be effectively suppressed when tuning the frequences to a same value.