Bursting dynamics triggered by the pulse-shaped explosion phenomenon in a parametrically and externally driven van der Pol–Mathieu system.

In this paper, bursting behaviors triggered by the pulse-shaped explosion (abbreviated as PSE) phenomenon and bifurcation structures are investigated in a parametrically and externally forced van der Pol–Mathieu system. The PSE, characterized by the pulse-shaped quantitative of the system solutions changing sharply at some values, is an innovative route to bursting oscillations reported recently. Three PSE-induced bursting types, namely intermittent "supHopf/supHopf-supHopf/supHopf" bursting via "PSE/PSE" hysteresis loop, "supHopf/supHopf" bursting via "PSE/PSE" hysteresis loop and "supHopf/supHopf" bursting via "supHopf/PSE" hysteresis loop, are investigated in detail by using the slow/fast analysis technology, time series analysis and phase diagram. We present a fact that the system parameters affect the positions of the PSE points, the types of the spiking states and the bursting forms. This paper adds the diversity of the bursting patterns triggered by the PSE and reveals some essential properties of bursting oscillations. In addition, the numerical simulations are used to test and verify the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]