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

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.

Dynamics of a simple third-order autonomous MLC circuit

“…Apart from the parameter-related evolution, the time sequence characteristics under fixed parameters can exhibit the special properties of the oscillation in nonlinear system. Bursting oscillation is a kind of complex dynamical behavior usually presented in multi-time scale systems [21]. It is characterized by alternating oscillations with large amplitudes and small ones over time.…”