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Hopf-like Bifurcation And Mixed Mode Oscillation In A Fractional-Order FitzHugh-Nagumo Model

Abstract : In this work we investigate the emergence of mixed-mode oscillations and canard explosion, in a planar fractionalorder FitzHugh-Nagumo model (FFHN). An algorithm, called Global-Local Canard Explosion Search Algorithm (GLCESA) is developed and used to investigate the existence of canard oscillations in the neighbourhoods of Hopf-like bifurcation points. the appearance of various patterns of solutions is revealed, with an increasing number of small-amplitude oscillations when two key parameters of the FFHN model are varied. The numbers of such oscillations versus the two parameters, respectively, are perfectly fitted using exponential functions. Finally, it is conjectured that chaos could occur in a 2-dimensional fractional-order autonomous dynamical system, with a fractional order close to one. After all, the article demonstrates that the FFHN Model is a very simple 2-dimensional model with an incredible ability to present the complex dynamics of neurons. Keywords: FitzHugh-Nagumo model, canard explosion, fractional-order system, mixed-mode oscillation, chaos.
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https://hal.archives-ouvertes.fr/hal-02883191
Contributeur : René Lozi <>
Soumis le : dimanche 22 novembre 2020 - 18:10:34
Dernière modification le : mercredi 2 décembre 2020 - 09:42:13

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Mohammed-Salah Abdelouahab, René Lozi. Hopf-like Bifurcation And Mixed Mode Oscillation In A Fractional-Order FitzHugh-Nagumo Model. AIP Conference Proceedings, American Institute of Physics, 2019, 2183, pp.100003-1 100003-4. ⟨10.1063/1.5136214⟩. ⟨hal-02883191⟩

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