Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation

Abstract

The complex bursting oscillation and bifurcation mechanisms in coupling systems of different scales have been a hot spot domestically and overseas. In this paper, we analyze the bursting oscillation of a generalized Duffing–Van der Pol system with periodic excitation. Regarding this periodic excitation as a slow-varying parameter, the system can possess two time scales and the equilibrium curves and bifurcation analysis of the fast subsystem with slow-varying parameters are given. Through numerical simulations, we obtain four kinds of typical bursting oscillations, namely, symmetric fold/fold bursting, symmetric fold/supHopf bursting, symmetric subHopf/fold cycle bursting, and symmetric subHopf/subHopf bursting. It is found that these four kinds of bursting oscillations are symmetric. Combining the transformed phase portrait with bifurcation analysis, we can observe bursting oscillations obviously and further reveal bifurcation mechanisms of these four kinds of bursting oscillations.

New Burst-Oscillation Mode in Paced One-Dimensional Excitable Systems

“…Since the fast-slow analysis method was proposed by Rinzel in 1985, which can effectively expose the formation and the mechanism of burst oscillation, great achievements have been made in this field. Distinct modes of burst oscillation were identified in different kinds of theoretical models and the corresponding mechanisms were further revealed (de Vries, 1998 ; Perc and Marhl, 2003 ; Zhang et al, 2007 ; Han and Bi, 2011 ; Yang and Hao, 2014 ; Vijay et al, 2019 ; Ma et al, 2021 ; Qian et al, 2021b ). For example, Vries discovered multiple bifurcations of bursting oscillations in a polynomial model (de Vries, 1998 ).…”

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

“…Based on the slow/fast decomposition analysis and Izhikevich's classification method, different types of the intermittent bursting are discovered and analyzed. For example, Qian et al [35] obtained four different intermittent symmetric bursting behaviors based on a generalized Duffing-van der Pol system. Ma et al [36] found two PSE-induced intermittent bursting forms and two non-PSE-induced compound bursting types of a Mathieu-van der Pol system.…”