Multi-time scale dynamics of mixed depolarization block bursting

Duan, Lixia; Liang, Tongtong; Yang, Zhao; Xi, Hongguang

doi:10.1007/s11071-020-05744-x

Cited by 21 publications

(4 citation statements)

References 41 publications

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“…In order to investigate the important question, many analytical methods have been proposed, such as experimental analysis [9,10], geometric singular perturbation method [11,12], numerical simulation method [13,14] and fast-slow decomposition analysis [15,16]. Based on these methods, many bursting patterns have been obtained, such as 'Homoclinic/Homoclinic' bursting [17], 'fold/fold' bursting [18], 'subHopf/LPC' bursting [19], 'fold/fold limit cycle' bursting [20] and 'Hopf/Hopf' bursting [21]. 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.…”

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%

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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show abstract

“…On the other hand, many important practical engineering problems also involve coupling of different time scales [13][14][15][16]. This type of system may cause mixed-mode oscillations, which are formed by a relatively large excursion and nearly harmonic small amplitude oscillation during every evolution period.…”

Section: Introductionmentioning

confidence: 99%

Complex Periodic Mixed-Mode Oscillation Patterns in a Filippov System

Zhang

Tang

2022

Mathematics

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The main task of this article is to study the patterns of mixed-mode oscillations and non-smooth behaviors in a Filippov system with external excitation. Different types of periodic spiral crossing mixed-mode oscillation patterns, i.e., “cusp-F−/fold-F−” oscillation, “cusp-F−/two-fold/two-fold/fold-F−” oscillation and “two-fold/fold-F−” oscillation, are explored. Based on the analysis of the equilibrium and tangential singularities of the fast subsystem, spiral crossing oscillation around the tangential singularities is investigated. Meanwhile, by combining the fast and slow analysis methods, we can observe that the cusp, two-fold and fold-cusp singularities play an important role in generating all kinds of complex mixed-mode oscillations.

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“…With the help of that, distinct forms of bursting vibrations have been proposed and investigated. For example, Duan et al [26] studied the mixed DB-bursting and its dynamical transitions, i.e. "fold/fold limit cycle" bursting, DB bursting and DB spiking, in pre-BötC.…”

Section: Introductionmentioning

confidence: 99%

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

Zhang

Tang

Wang

2022

Preprint

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This paper investigates the bursting oscillations of a externally and parametrically forced Rayleigh-Duffing oscillator, in which three intermittent bursting types and one normal bursting type, namely intermittent “supHopf/supHopf-supHopf/supHopf” bursting, intermittent “fold/Homoclinic-Homoclinic/supHopf” bursting, intermittent “fold/Homoclinic-supHopf/supHopf” bursting and “fold/Homoclinic” bursting, are analyzed respectively. Recognizing the excitations as slow-varying state variables, the corresponding autonomous system can be exhibited and the bifurcation characteristics is briefly investigated, in particular, the Homoclinic bifurcation is analyzed by means of the Melnikov criterion. This paper shows that the dynamical behaviors of the excited Rayleigh-Duffing oscillator is touchy to the chosen of system parameters, different parameter conditions lead to distinct bifurcation structures that result in the trajectory approaching to different stable attractors and the appearance of different bursting forms. Our study increases the variousness of bursting oscillations and deepens the cognition of the generation mechanism of bursting dynamics. Lastly, the accuracy of the analysis presented in this paper is fully vindicated by the numerical simulations.

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Multi-time scale dynamics of mixed depolarization block bursting

Cited by 21 publications

References 41 publications

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

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

Complex Periodic Mixed-Mode Oscillation Patterns in a Filippov System

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

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