Complex bursting dynamics of a Mathieu-van der Pol-Duffing energy harvester

Ma, Xindong; Jiang, Wen-An; Zhang, Xiaofang; Han, Xiujing; Bi, Qinsheng

doi:10.1088/1402-4896/abcad1

Cited by 28 publications

(8 citation statements)

References 66 publications

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“…Based on the analysis of characteristic polynomial formula equation (12), there are many local bifurcations of system (8), which constitute the focus of our research in this article. Mainly three kinds of bifurcations can be obtained: fold bifurcations, Hopf bifurcations and Homoclinic bifurcations, therefore, we will analyze the conditions of these three kinds of bifurcations and give the numerical simulations for the stabilities and bifurcations in this part.…”

Section: Bifurcation Analysismentioning

confidence: 99%

“…In the field of Physics, Bao et al [11] revealed the bifurcation mechanism in a novel third-order autonomous memristor diode bridge. Ma et al [12] explored the complex mechanisms of different periodic bursting behaviors based on a Mathieu-van der Pol-Duffing energy harvester with parametric excitation. Different from the above two scholars' research on periodic bursting oscillation, Alombah et al [13] investigated some complicated nonlinear behaviors in a four-dimensional multiscroll autonomous memristor based on a chaotic system.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao¹,

Ma²,

Zhang³

et al. 2022

Phys. Scr.

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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.

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Section: Bifurcation Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Zhao¹,

Ma²,

Zhang³

et al. 2022

Phys. Scr.

Self Cite

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“…Wang et al [28] first observed the quasi-periodic, periodic and chaotic bursting oscillation produced by cascaded pitchfork and Hopf bifurcations. Ma et al [29] explored the bursting oscillations induced by bifurcation delay phenomenon and the dynamical evolutions among the different bursting patterns. Yuan et al [30] presented a new meminductor system and investigated the bursting oscillations theoretically and experimentally.…”

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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“…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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Complex bursting dynamics of a Mathieu-van der Pol-Duffing energy harvester

Cited by 28 publications

References 66 publications

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

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

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