Bifurcation characteristics and bursting oscillation of Duffing-Van der Pol oscillator

In this paper, we study the bifurcation characteristics and bursting oscillation of the Duffing-Van der Pol system with periodic excitation. Due to the different frequency scales between the excitation frequency and the natural frequency in the oscillator, when the periodic excitation changes slowly with time, the system is considered as a slow subsystem, and when it is fixed, the system is considered as a fast subsystem. We analyze the bifurcation characteristics of the fast subsystem and use the slowly varying parameter as the bifurcation parameter to show how the bursting oscillations are generated. Furthermore, the phase diagram and time-history diagram of fold-fold bursting oscillation, fold-subHopf bursting oscillation, supHopf-supHopf bursting oscillation, and homoclinic-homoclinic bursting oscillation are given by numerical simulation. Combined with the fig-ures, it is found that these four kinds of bursting oscillations with bifurcation delay phenomenon are symmetrical and further reveal the bifurcation mechanisms of these four kinds of bursting oscillations.