Bursting oscillations induced by bistable pulse-shaped explosion in a nonlinear oscillator with multiple-frequency slow excitations

This paper investigates bursting dynamics of a Rayleigh oscillator with multiple-frequency slow excitations, in which two different bursting patterns related to the bistable pulse-shaped explosion (PSE) are obtained. Typically, the PSE, a novel sharp transition behavior reported recently, can be observed in the Rayleigh oscillator. We show that if there is an initial phase difference -pi/2 between the slow excitations, two coexisting solution branches exhibiting PSE, which we call bistable PSE, may be created in the fast subsystem. Then, the route to bursting by the bistable PSE is analyzed, and two different bursting patterns, i.e., bursting of point-point type and bursting of cycle-cycle type, are obtained. Our findings show that the initial phase difference of excitations may have great effects on PSE, which thus plays an important role in transitions to different attractors and complex bursting dynamics.