Geometrical Model of Spiking and Bursting Neuron on a Mug-Shaped Branched Manifold

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Detail(s)

Original languageEnglish
Article number2030044
Journal / PublicationInternational Journal of Bifurcation and Chaos
Volume30
Issue number15
Publication statusPublished - 15 Dec 2020

Abstract

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.

Research Area(s)

  • Bursting oscillation, chaos, horseshoe attractor, Poincaré map, spike