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Article Dans Une Revue International Journal of Bifurcation and Chaos (IJBC) Année : 2020

Geometrical model of spiking and bursting neuron on a mug-shaped branched manifold

Mohamed Gheouali
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Tounsia Benzekri
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René Lozi
Guanrong Chen
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Résumé

Based on the Hodgkin-Huxley and Hindmarsh-Rose models, this paper proposes a geometric phenomenological model of bursting neuron in its simplest form, describing the dynamic motion on a mug-shaped branched manifold, which is a cylinder tied to a ribbon. Rigorous mathematical analysis is performed on the nature of the bursting neuron solutions: the number of spikes in a burst, the periodicity or chaoticity of the bursts, etc. The model is then generalized to obtain mixing burst of any number of spikes. Finally, an example is presented to verify the theoretical results.
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Dates et versions

hal-02878585 , version 1 (23-06-2020)

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Mohamed Gheouali, Tounsia Benzekri, René Lozi, Guanrong Chen. Geometrical model of spiking and bursting neuron on a mug-shaped branched manifold. International Journal of Bifurcation and Chaos (IJBC), 2020, 30 (5), pp.2030044. ⟨10.1142/S021812742030044X⟩. ⟨hal-02878585⟩
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