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Compound bursting behaviors in a forced Mathieu-van der Pol-Duffing system

Author

Listed:
  • Ma, Xindong
  • Xia, Daixian
  • Jiang, Wenan
  • Liu, Mao
  • Bi, Qinsheng

Abstract

The mechanism of compound bursting behaviors of a forced Mathieu-van der Pol-Duffing system is explored. Four compound bursting types and one typical relaxation oscillation, i.e., compound “Homoclinic/Homoclinic” bursting, compound “fold/fold-cycle” bursting, compound “subHopf/fold-cycle” bursting via “fold/fold” hysteresis loop, compound “supHopf/supHopf” bursting via “fold/fold” hysteresis loop and “fold/fold” bursting, are investigated. We find that different parameter values result in different repetitive spiking states, which lead to different bursting patterns. Our research provides more possible routes to compound bursting dynamics, and strengthens a better understanding of the compound bursting behaviors.

Suggested Citation

  • Ma, Xindong & Xia, Daixian & Jiang, Wenan & Liu, Mao & Bi, Qinsheng, 2021. "Compound bursting behaviors in a forced Mathieu-van der Pol-Duffing system," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003210
    DOI: 10.1016/j.chaos.2021.110967
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    References listed on IDEAS

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    1. Zhou, Chengyi & Xie, Fei & Li, Zhijun, 2020. "Complex bursting patterns and fast-slow analysis in a smallest chemical reaction system with two slow parametric excitations," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. 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. Song, Jian & Liu, Shenquan & Wen, Qixiang, 2022. "Geometric analysis of the spontaneous electrical activity in anterior pituitary corticotrophs," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    2. Zhao, Heqi & Ma, Xindong & Yang, Weijie & Zhang, Zhao & Bi, Qinsheng, 2023. "The mechanism of periodic and chaotic bursting patterns in an externally excited memcapacitive system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Zhang, Xiaofang & Li, Hongqing & Jiang, Wenan & Chen, Liqun & Bi, Qinsheng, 2022. "Exploiting multiple-frequency bursting of a shape memory oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    4. Danjin Zhang & Youhua Qian, 2023. "Bursting Oscillations in General Coupled Systems: A Review," Mathematics, MDPI, vol. 11(7), pages 1-16, April.

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