Complex bursting dynamics in the cubic-quintic Duffing-van der Pol system with two external periodic excitations

Ma, Xindong; Bi, Qinsheng; Wang, Lifeng

doi:10.1007/s11012-022-01544-2

Cited by 8 publications

(1 citation statement)

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“…However, most of the achievements are related to the time-domain multiple timescale, in other words, bursting oscillations are induced by different change rates between/among different state variables in the autonomous systems. While for the periodic excitation systems, if there is a magnitude difference between the excitation frequency and the system natural frequency, the systems also exhibit the bursting oscillations [22,23]. Due to the presence of time t in the system, no obvious slow and fast variables exist, the standard fast-slow decomposition analysis method cannot be directly used to analyze the mechanism of the bursting oscillations.…”

Section: Introductionmentioning

confidence: 99%

Analysis on the symmetric fast-slow behaviors in a van der Pol-Duffing-Jerk oscillator

Lyu,

Li,

Huang

et al. 2023

Phys. Scr.

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The study of bursting oscillations induced by frequency-domain multiscale effect is one of the key scientific issues in the theoretical analysis of circuit systems. In this paper, we explore the mechanism of the bursting oscillations of a van der Pol-Duffing-Jerk circuit oscillator with slow-changing parametric and external periodic excitations. Three typical bursting modes, namely, left-right symmetric “subHopf/fold limit cycle” bursting, origin symmetric “fold/fold limit cycle” bursting and origin symmetric “fold/subHopf/fold limit cycle” bursting, are presented. The slowly changing excitation is treated as a generalized state variable to analyze the influence on the critical manifolds of the equilibria and bifurcations. The critical conditions of fold and Hopf bifurcations are computed by using the bifurcation theory, and two typical bifurcation structures are obtained according to the position of different bifurcation curves. Based on the bifurcation analysis, we investigate the appearance and dynamicalal evolutions of the different bursting oscillations with the variation of the external excitation amplitude. It is pointed that not only the bifurcation structures but also the distance between the fold and Hopf bifurcation points can affect the bursting patterns. We find the directions of the trajectories and the bursting types are sensitive to the values of the external excitation amplitude. Furthermore, we reveal the mechanism of the bursting oscillations by overlapping the trajectories on (,x)-plane onto the corresponding bifurcation structures. Numerical simulations are also presented to prove the correctness of the theoretical analysis in our study.

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Section: Introductionmentioning

confidence: 99%