Bifurcation mechanism of bursting oscillations in parametrically excited dynamical system

•Different types of bursting oscillations are obtained.•The bifurcation mechanism of bursting oscillations is presented.•The evolution of bursting oscillations is explored.

The evolution of bursting oscillations in a parametrically excited dynamical system with order gap between the excited frequency and the natural frequency is investigated in this paper. By regarding the periodic excited term as a slow-varying parameter, different forms of bifurcations of the system are obtained. Base on the overlap between the bifurcation diagram and the phase portrait, the mechanism of different types of bursting oscillations are obtained. Furthermore, some phenomena in bursting oscillations such as symmetry breaking behavior are explained through the bifurcations occurring at the transitions between the quiescent state (QS) and spiking state (SP).