Chaotic dynamics of an extended Duffing-van der Pol system with a non-smooth perturbation and parametric excitation

Abstract

Abstract Chaotic dynamics of a fifth-order extended Duffing-van der Pol system with a non-smooth periodic perturbation and parametric excitation are investigated both analytically and numerically in this paper. With the Fourier series, the system is expanded to the equivalent smooth system. The Melnikov perturbation method is used to derive the horseshoe chaos condition in the cases of homoclinic and heteroclinic intersections. The chaotic features for different system parameters are investigated in detail. The monotonic variation of the coefficients of parametric excitation and non-smooth periodic disturbance is found. With numerical methods, we validate the analytical results obtained by Melnikov’s method. The impact of initial conditions is carefully analyzed by basins of attraction and the effect of non-smooth periodic disturbance on the basin of attraction is also investigated. Besides, the effect of different parameters on the bifurcation pathway into chaotic attractors is examined.