Geometrical model of spiking and bursting neuron on a mug-shaped branched manifold
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.
Domaines
Systèmes dynamiques [math.DS]
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Gheouali_Benzekri_Lozi_Chen_Geometrical_model.pdf (1.42 Mo)
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