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

Authors

Nkounga,  I.B. Tagne
Potsdam Institute for Climate Impact Research;

Xia,  Yibo
Potsdam Institute for Climate Impact Research;

/persons/resource/yanchuk

Yanchuk,  Serhiy
Potsdam Institute for Climate Impact Research;

Yamapi,  R.
External Organizations;

/persons/resource/Juergen.Kurths

Kurths,  Jürgen
Potsdam Institute for Climate Impact Research;

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Citation

Nkounga, I. T., Xia, Y., Yanchuk, S., Yamapi, R., Kurths, J. (2023): Generalized FitzHugh–Nagumo model with tristable dynamics: Deterministic and stochastic bifurcations. - Chaos, Solitons and Fractals, 175, Part 1, 114020.
https://doi.org/10.1016/j.chaos.2023.114020


Cite as: https://publications.pik-potsdam.de/pubman/item/item_29456
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.