Bursting dynamics and the bifurcation mechanism of a modified Rayleigh-van der Pol-Duffing oscillator

Abstract

Abstract In this paper, complex bursting patterns in a modified Rayleigh-van der Pol-Duffing oscillator(abbreviated as MRPDO) under the simultaneous effect of parametric and external excitations are given theoretically by fast-slow analysis method. Four different kinds of bursting oscillations, i.e. bursting of compound asymmetric ‘Homoclinic/Homoclinic’ type, bursting of compound asymmetric ‘delayed Homoclinic/Homoclinic’ type, bursting of compound ‘fold/delayed Homoclinic connection/supHopf-supHopf/supHopf’ type and bursting of ‘fold/delayed Homoclinic’ type, are studied. For bursting of compound ‘fold/delayed Homoclinic connection/supHopf-supHopf/supHopf’ type, we explain the delay generation mechanism. Based on the characteristics of the Homoclinic-limit cycles, we propose the concepts of the approximate quiescent state and peculiar limit cycle attractor.