Chaos Control in Duffing-Van Der Pol System

In this paper we present analytical and numerical results concerning the inhibition of chaos in DufŒng-van der Pol system with Œth nonlinear-restoring force and two external forcing terms. We theoretically give parameter-space regions interval of initial phase difference on the basis of Melnikov methods proposed in, where homoclinic chaos can be suppressed. Numerical simulation results show the consistence with the theoretical analysis and Œnd that the chaotic motions can be controlled to period-motions by adjusting phase difference and amplitude of second forcing excitation. Moreover, we give the distribution of maximum Lyapunov exponents(LE) in parameter plane, which shows the regions of non-chaotic states (non-positive LE) and chaotic states (positive LE).