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

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

Chaos, Solitons & Fractals, 2023, vol. 175, issue P1

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.

Keywords: FitzHugh–Nagumo; Conductance-based neuronal model; Tristability; Quiescent state; Subthreshold oscillations; Spike generation; Channel noise; Probability distribution (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:175:y:2023:i:p1:s0960077923009219

DOI: 10.1016/j.chaos.2023.114020

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