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Dynamical behavior of simplified FitzHugh-Nagumo neural system driven by Lévy noise and Gaussian white noise

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  • Guo, Yongfeng
  • Wang, Linjie
  • Wei, Fang
  • Tan, Jianguo

Abstract

In this paper, the dynamical behavior of simplified FitzHugh-Nagumo (FHN) neuron system under the co-excitation of Lévy noise and Gaussian white noise are studied. Consideration from two aspects: the mean first-passage time (MFPT) and the probability density function (PDF) of the first-passage time (FPT). Using Janicki–Weron algorithm to generate Lévy noise, and through the fourth-order Runge–Kutta algorithm to simulate the system response, the FPT of the 2 × 104 response tracks are calculated, and then the MFPT and the PDF are obtained. Finally, the effects of the multiplicative Gaussian noise and additive Lévy noise on the MFPT and PDF of the FPT are discussed. In addition, it is found that the noise enhanced stability (NES) and resonance activation (RA) phenomena in the system.

Suggested Citation

  • Guo, Yongfeng & Wang, Linjie & Wei, Fang & Tan, Jianguo, 2019. "Dynamical behavior of simplified FitzHugh-Nagumo neural system driven by Lévy noise and Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 118-126.
    • Handle: RePEc:eee:chsofr:v:127:y:2019:i:c:p:118-126
    DOI: 10.1016/j.chaos.2019.06.031
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    Cited by:

    1. Zhang, Gang & Shu, Yichen & Zhang, Tianqi, 2022. "The study on dynamical behavior of FitzHugh–Nagumo neural model under the co-excitation of non-Gaussian and colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
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    3. Lin, Yi & Liu, Wenbo & Hang, Cheng, 2023. "Revelation and experimental verification of quasi-periodic bursting, periodic bursting, periodic oscillation in third-order non-autonomous memristive FitzHugh-Nagumo neuron circuit," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Hua, Mengjiao & Wu, Yu, 2022. "Transition and basin stability in a stochastic tumor growth model with immunization," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).

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