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Dynamical complexity of FitzHugh–Nagumo neuron model driven by Lévy noise and Gaussian white noise

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  • Guo, Yongfeng
  • Wang, Linjie
  • Dong, Qiang
  • Lou, Xiaojuan

Abstract

In this paper, on the basis of information theory measures (statistical complexity and normalized Shannon entropy), the dynamical complexity of FitzHugh–Nagumo (FHN) neuron model under the co-excitation of Lévy noise and Gaussian white noise is studied. Because the potential function of the neuron system is asymmetric, we consider not only the total residence time interval of the system, but also the residence time interval of the left and right potential wells respectively. Here, we use Bandt–Pompe algorithm to calculate the three interval sequences, and obtain the statistical complexity and normalized Shannon entropy of the total system as well as the left and right potential wells. Finally, the effects of additive noise intensity, multiplicative noise intensity and system parameter on complexity of system are analyzed. We find that the total dynamical complexity of the system is obviously different from that of a single potential well. In addition, Gaussian white noise and Lévy noise have different effects on the complexity of the system.

Suggested Citation

  • Guo, Yongfeng & Wang, Linjie & Dong, Qiang & Lou, Xiaojuan, 2021. "Dynamical complexity of FitzHugh–Nagumo neuron model driven by Lévy noise and Gaussian white noise," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 430-443.
    • Handle: RePEc:eee:matcom:v:181:y:2021:i:c:p:430-443
    DOI: 10.1016/j.matcom.2020.09.026
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    1. Rafal Weron, 1996. "Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"," HSC Research Reports HSC/96/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    2. O. A. Rosso & C. Masoller, 2009. "Detecting and quantifying temporal correlations in stochastic resonance via information theory measures," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 37-43, May.
    3. Yong Xu & Juanjuan Li & Jing Feng & Huiqing Zhang & Wei Xu & Jinqiao Duan, 2013. "Lévy noise-induced stochastic resonance in a bistable system," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(5), pages 1-7, May.
    4. Weron, Rafal, 1996. "On the Chambers-Mallows-Stuck method for simulating skewed stable random variables," Statistics & Probability Letters, Elsevier, vol. 28(2), pages 165-171, June.
    5. A. Dubkov & B. Spagnolo, 2008. "Verhulst model with Lévy white noise excitation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(3), pages 361-367, October.
    6. Lamberti, P.W & Martin, M.T & Plastino, A & Rosso, O.A, 2004. "Intensive entropic non-triviality measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 119-131.
    7. Upadhyay, Ranjit Kumar & Paul, Chinmoy & Mondal, Argha & Vishwakarma, Gajendra K., 2018. "Estimation of biophysical parameters in a neuron model under random fluctuations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 364-373.
    8. Xu, Yong & Wu, Juan & Du, Lin & Yang, Hui, 2016. "Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 91-100.
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