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A Density Model for a Population of Theta Neurons

Gregory Dumont 1, * Jacques Henry 1, 2 Carmen Oana Tarniceriu 3 
* Corresponding author
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, IHU-LIRYC
Abstract : Population density models that are used to describe the evolution of neural populations in a phase space are closely related to the single neuron model that describes the individual trajectories of the neurons of the population and which give in particular the phase-space where the computations are made. Based on a transformation of the quadratic integrate and fire single neuron model, the so-called theta-neuron model is obtained and we shall introduce in this paper a corresponding population density model for it. Existence and uniqueness of a solution will be proved and some numerical simulations are presented. The results of existence are compared to previous results of existence or nonexistence (burst) for populations of leaky integrate and fire neurons.
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Submitted on : Thursday, September 25, 2014 - 5:32:21 PM
Last modification on : Thursday, January 20, 2022 - 5:31:36 PM

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Gregory Dumont, Jacques Henry, Carmen Oana Tarniceriu. A Density Model for a Population of Theta Neurons. Journal of Mathematical Neuroscience, BioMed Central, 2014, 4 (2), ⟨10.1186/2190-8567-4-2⟩. ⟨hal-01068536⟩



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