2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Collection 2022 - T1 - WS2 - Mathematical modeling and statistical analysis in neuroscience

Organizer(s) Ditlevsen, Susanne ; Faugeras, Olivier ; Galves, Antonio ; Reynaud-Bouret, Patricia ; Salort, Delphine ; Shinomoto, Shigeru

Date(s) 31/01/2022 - 04/02/2022

linked URL https://indico.math.cnrs.fr/event/6532/

00:00:00 / 00:00:00

28 30

A multiple time renewal equation for neural assemblies with elapsed time model

By Nicolas Torres

We introduce and study an extension of the classical elapsed time equation in the context of neuron populations that are described by the elapsed time since the last discharge, i.e., the refractory period. In this extension we incorporate the elapsed since the penultimate discharge and we obtain a more complex system of integro-differential equations. For this new system we prove convergence to stationary state by means of Doeblin’s theory in the case of weak non-linearities in an appropriate functional setting, inspired by the case of the classical elapsed time equation. Moreover, we present some numerical simulations to observe how different firing rates can give different types of behaviors and to contrast them with theoretical results of both classical and extended models.

Information about the video

Date of recording 04/02/2022
Date of publication 04/02/2022
Institution IHP
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2022.T1.WS2.028
Cite this video Torres, Nicolas (04/02/2022). A multiple time renewal equation for neural assemblies with elapsed time model. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.028
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.028

Bibliography

José A Cañizo and Havva Yoldaş / Asymptotic behaviour of neuron population models structured by elapsed-time. Nonlinearity, vol. 32 n°2 (2019), p. 464.
Nicolás Torres, Benoît Perthame, and Delphine Salort / A multiple time renewal equation for neural assemblies with elapsed time model. arXiv preprint (2021), arXiv:2108.10577.

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