Chaos Control in Duffing-Van Der Pol System

Abstract

In this paper we present analytical and numerical results concerning the inhibition of chaos in Duffing-van der Pol system with fifth 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 [6], where homoclinic chaos can be suppressed. Numerical simulation results show the consistence with the theoretical analysis and find 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).