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Complex mixed-mode oscillations based on a modified Rayleigh-Duffing oscillator driven by low-frequency excitations

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  • Zhang, Chun
  • Ma, Xindong
  • Bi, Qinsheng

Abstract

The complex mixed-mode oscillation patterns are proposed and analyzed in a modified Rayleigh-Duffing oscillator based on the bifurcation theory in this paper. Four mixed-mode oscillations, namely “Homoclinic/Homoclinic-Homoclinic/Homoclinic” intermittent type, “fold/Homoclinic-Homoclinic/supHopf” intermittent type, “fold/Homoclinic-supHopf/supHopf” intermittent type and “fold/Homoclinic” type, are discussed in detail. Considering the low frequency excitations as slow-changing state variables, a modified autonomous system is obtained. The bifurcation characteristics of the fast subsystem are presented briefly by using the bifurcation theory. Then, we investigate the generation principle of the bifurcation delay phenomenon that performs a critical role in the production of two mixed-mode oscillations. This paper presents a fact that the dynamical behaviors are sensitive to the values of the system parameters and the parameters determine different forms of the repetitive spiking states that leads to different patterns of the mixed-mode oscillations. In addition, the theoretical analysis and numerical simulations are compared to illustrate the correctness of this paper.

Suggested Citation

  • Zhang, Chun & Ma, Xindong & Bi, Qinsheng, 2022. "Complex mixed-mode oscillations based on a modified Rayleigh-Duffing oscillator driven by low-frequency excitations," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922003940
    DOI: 10.1016/j.chaos.2022.112184
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    References listed on IDEAS

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    1. Bao, B.C. & Wu, P.Y. & Bao, H. & Xu, Q. & Chen, M., 2018. "Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in third-order autonomous memristive oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 161-170.
    2. Yu, Yue & Zhang, Cong & Chen, Zhenyu & Lim, C.W., 2020. "Relaxation and mixed mode oscillations in a shape memory alloy oscillator driven by parametric and external excitations," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Youhua Qian & Danjin Zhang & Bingwen Lin & Pietro De Lellis, 2021. "Bursting Oscillation and Its Mechanism of a Generalized Duffing–Van der Pol System with Periodic Excitation," Complexity, Hindawi, vol. 2021, pages 1-13, July.
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    1. Sharma, Sanjeev Kumar & Mondal, Arnab & Mondal, Argha & Aziz-Alaoui, M.A. & Upadhyay, Ranjit Kumar & Ma, Jun, 2022. "Emergence of Canard induced mixed mode oscillations in a slow–fast dynamics of a biophysical excitable model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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