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

Author:

Zhao Heqi,Ma XindongORCID,Zhang Bin,Bi QinshengORCID

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.

Funder

National Natural Science Foundation of China

Publisher

IOP Publishing

Subject

Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics

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