Analysis of chaotic behavior in the extended Duffing–Van der Pol system subject to additive non-symmetry biharmonical excitation

The problem of controlling chaos for a certain class of extended Duffing–Van der Pol system under additive non-symmetry biharmonical excitation with specific parameters is investigated by the way of random phase parallel movement in this paper. The results show that the initial phase has some important effect on controlling chaos and noises can increase the robustness of controlling chaos. With specific parameters, the adjustment phase of the first harmonical excitation and the noise intensity of the second non-symmetry harmonical excitation do not suppress chaos in the system. In order to control chaos, the diagrams of phase versus amplitude of the second harmonical excitation were drawn on the basis of the fact that chaos can be suppressed when the sign of the top Lyapunov exponent is negative. The robustness and mechanism of suppressing chaotic motion with random phase or noise were also initially discussed. The author put forward a method called random phase parallel movement to control chaos. The availability of this method was validated via the curve of the top Lyapunov exponent, phase diagram, Poincare surface of the section and time evolution.