一个Van Der Pol-Duffing系统的混沌与控制

Chaos and Control in a Van Der Pol-Duffing System

研究了Van der Pol-Duffing振子的混沌动力学行为,应用直接微扰法构造了系统的通解,由该通解获得了预测混沌出现的Melnikov判据.在非微扰情形,相图和相应Poincaré截面的演化结果表明:系统阻尼和外驱动力的变化都可以导致系统由倍周期分叉进入混沌状态,当频率参数取相同值时,系统混沌被完全抑制.

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.