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Compound bursting dynamics in a parametrically and externally excited mechanical system

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  • Wei, Mengke
  • Jiang, Wenan
  • Ma, Xindong
  • Zhang, Xiaofang
  • Han, Xiujing
  • Bi, Qinsheng

Abstract

This paper aims to report complex bursting dynamics in a parametrically and externally excited mechanical system. Typically, two compound bursting patterns, i.e., bursting of “supHopf/homoclinic-fold/supHopf” type and bursting of “supHopf/supHopf-fold/supHopf” type, composed of two different clusters during each period of bursting, can be observed in this system. To begin with, the generation of each of the two clusters in compound bursting of “supHopf/homoclinic-fold/supHopf” type is investigated by the fast-slow analysis. Then, a two-parameter bifurcation diagram is plotted to investigate the transition of the compound bursting. We show that there are two originally disunited active areas, which may inosculate as a whole by homoclinic bifurcations if the system parameter varies properly. Based on this, a different type of compound bursting, i.e., bursting of “supHopf/supHopf-fold/supHopf” type, is revealed.

Suggested Citation

  • Wei, Mengke & Jiang, Wenan & Ma, Xindong & Zhang, Xiaofang & Han, Xiujing & Bi, Qinsheng, 2021. "Compound bursting dynamics in a parametrically and externally excited mechanical system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309966
    DOI: 10.1016/j.chaos.2020.110605
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    References listed on IDEAS

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    1. Chen, Zhenyang & Chen, Fangqi, 2020. "Mixed mode oscillations induced by bi-stability and fractal basins in the FGP plate under slow parametric and resonant external excitations," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. Razvan, Mohammad Reza & Yasaman, Somaye, 2020. "Emergence of bursting in two coupled neurons of different types of excitability," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    3. Li, J. & Miao, S.F. & Zhang, W., 2007. "Analysis on bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 960-976.
    4. Wen, Zihao & Li, Zhijun & Li, Xiang, 2019. "Bursting oscillations and bifurcation mechanism in memristor-based Shimizu–Morioka system with two time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 58-70.
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    Cited by:

    1. Wei, Mengke & Han, Xiujing & Bi, Qinsheng, 2022. "Sufficient conditions and criteria for the pulse-shaped explosion related to equilibria in a class of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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