A new route to pulse-shaped explosion and its induced bursting dynamics

Abstract

Pulse-shaped explosion (PSE), characterized by pulse-shaped sharp quantitative changes in relation to the variation of system parameters, is a novel dynamical mechanism underlying the occurrence of bursting oscillations. In previous works, the generation of PSE was found to be related to a fold bifurcation of the critical escape transitions. In this paper, we report a new route to PSE based on the externally and parametrically excited Rayleigh system. We show that the forward and reverse C-shaped equilibrium curves, exhibiting two symmetrical fold points, can be observed in the fast subsystem. In particular, we find that the two opposite C-shaped equilibrium curves are tangent at the fold point of fold curves, which leads to an X-shaped equilibrium curve that is extremely steep near the tangent point. With the disappearance of the fold point of fold curves, the X-shaped equilibrium curve splits into two separate branches, both of which show pulse-shaped quantitative changes. As a result, two symmetrical PSEs are created. Based on this, a new route to PSE by the fold bifurcation of fold curves is presented. Finally, we briefly investigate bursting dynamics induced by the PSE and the effects of parametric excitation amplitude on bursting dynamics.