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The study on dynamical behavior of FitzHugh–Nagumo neural model under the co-excitation of non-Gaussian and colored noise

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  • Zhang, Gang
  • Shu, Yichen
  • Zhang, Tianqi

Abstract

The dynamical behavior of the one-dimensional FitzHugh–Nagumo (FN) neural model under the co-excitation of cross-correlation multiplicative non-Gaussian noise and additive colored noise are investigated in this paper. Firstly, the one-dimensional Langevin equation of the FN model can be obtained by using the adiabatic elimination method. Then, the approximate Fokker–Planck equation (AFPE) is derived with functional methods, and the expressions of steady-state probability density function (PDF) and the mean first-passage time (MFPT) are obtained. Finally, the effects of different parameters on PDF and MFPT are discussed as a reflection of the properties of the FN neural model. Moreover, under certain conditions, noise enhanced stability (NES) effects can be induced by noise.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:587:y:2022:i:c:s0378437121008244
    DOI: 10.1016/j.physa.2021.126551
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    References listed on IDEAS

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    1. Tessone, Claudio J. & Wio, Horacio S., 2007. "Stochastic resonance in an extended FitzHugh–Nagumo system: The role of selective coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(1), pages 46-54.
    2. Singh, R.K., 2017. "Noise enhanced stability of a metastable state containing coupled Brownian particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 445-450.
    3. Lu, Lulu & Ge, Mengyan & Xu, Ying & Jia, Ya, 2019. "Phase synchronization and mode transition induced by multiple time delays and noises in coupled FitzHugh–Nagumo model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Yao, Yuangen & Ma, Chengzhang & Wang, Canjun & Yi, Ming & Gui, Rong, 2018. "Detection of sub-threshold periodic signal by multiplicative and additive cross-correlated sine-Wiener noises in the FitzHugh–Nagumo neuron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1247-1256.
    5. Zhang, Huiqing & Xu, Wei & Xu, Yong, 2009. "The study on a stochastic system with non-Gaussian noise and Gaussian colored noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(6), pages 781-788.
    6. Sergey M. Bezrukov & Igor Vodyanoy, 1997. "Stochastic resonance in non-dynamical systems without response thresholds," Nature, Nature, vol. 385(6614), pages 319-321, January.
    7. Liang, G.Y. & Cao, L. & Wu, D.J., 2004. "Approximate Fokker–Planck equation of system driven by multiplicative colored noises with colored cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 371-384.
    8. Sergey M. Bezrukov & Igor Vodyanoy, 1997. "Erratum: Stochastic resonance in non-dynamical systems without response thresholds," Nature, Nature, vol. 386(6626), pages 738-738, April.
    9. 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.
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