Chaos analysis for a class of impulse Duffing-van der Pol system

Abstract

Chaotic dynamics of an impulse Duffing-van der Pol system is studied in this paper. With the Melnikov method, the existence condition of transversal homoclinic point is obtained, and chaos threshold is presented. In addition, numerical simulations including phase portraits and time histories are carried out to verify the analytical results. Bifurcation diagrams are also given, from which it can be seen that the system may undergo chaotic motions through period doubling bifurcations.