Chaos Controlling and Bifurcation of Van der Pol-Duffing System

The research selected a set of parameters which could conduce chaos of Van der Pol - Duffing system by averaging method and Melnikov-Holmes method.The paper investigated the influence on the global dynamics behaviors by the change of forced excitation.The very rich and multiplex nonlinear dynamics of the Van der Pol-Duffing oscillator was investigated by theoretical and numerical simulation with the tiny change of the system parameters.The characteristics of chaos attractors of the system were analyzed by the Poincare map.By simulating the bifurcation diagrams,we demonstrated exactly periodic and chaos motions under the presented parameters.By computing time series' Lyapunov exponents and Lyapunov dimensions of Van der Pol- Duffing oscillator,we analyzed the chaos characteristics of the system.Finally,two effective controlling methods were applied to controlling chaos of the system.