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Generalized FitzHugh–Nagumo model with tristable dynamics: Deterministic and stochastic bifurcations

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  • Nkounga, I.B. Tagne
  • Xia, Yibo
  • Yanchuk, Serhiy
  • Yamapi, R.
  • Kurths, Jürgen

Abstract

We propose an extension of the Fitzhugh-Nagumo model, which possesses a regime of three coexisting stable states: resting equilibrium and two stable oscillatory states. Such a regime is absent in the original Fitzhugh-Nagumo model but it is known to exist in higher-dimensional conductance based neuronal models. Thus, the proposed system provides a simpler two-dimensional model with such a property. Using numerical bifurcation analysis as well as Lindsted’s method, we explore parameter regions and bifurcations leading to the tristability. Considering the effects of channel fluctuations as Gaussian white noise, phenomenological bifurcations of the corresponding stochastic system are analyzed using a Fokker–Planck approach. We investigate how the interplay between the system parameters and the noise intensity induces a switching of neural activities between silence, subthreshold, and spiking.

Suggested Citation

  • Nkounga, I.B. Tagne & Xia, Yibo & Yanchuk, Serhiy & Yamapi, R. & Kurths, Jürgen, 2023. "Generalized FitzHugh–Nagumo model with tristable dynamics: Deterministic and stochastic bifurcations," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    • Handle: RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923009219
    DOI: 10.1016/j.chaos.2023.114020
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    References listed on IDEAS

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    1. I.B., Tagne nkounga & F.M., Moukam kakmeni & R., Yamapi, 2022. "Birhythmic oscillations and global stability analysis of a conductance-based neuronal model under ion channel fluctuations," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    2. Antti Saarinen & Marja-Leena Linne & Olli Yli-Harja, 2008. "Stochastic Differential Equation Model for Cerebellar Granule Cell Excitability," PLOS Computational Biology, Public Library of Science, vol. 4(2), pages 1-11, February.
    3. Joshua H Goldwyn & Eric Shea-Brown, 2011. "The What and Where of Adding Channel Noise to the Hodgkin-Huxley Equations," PLOS Computational Biology, Public Library of Science, vol. 7(11), pages 1-9, November.
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