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

23 30

Front initiation in continuous neural fields

By Grégory Faye

In this talk, I shall present some recent and ongoing results regarding the question of front initiation in continuous scalar neural fields. The problem is to characterize, given a localized initial condition, the long-time dynamic of the solution of the associated Cauchy problem. When the underlying kinetics of the homogenous problem is of bistable type with two stables states, say $u = 0$ and $u = 1$, with $u = 1$ more favorable than $u = 0$, one expects that small (in some appropriate sense) localized initial condition will lead to uniform convergence of the solution towards $u = 0$ (this is referred to as extinction) and large localized initial condition will lead to convergence on compact sets towards $u = 1$ (this is referred to as propagation). The identification of a threshold between extinction/propagation within a given one parameter family of localized initial condition is a well-known difficult problem, even for local bistable reaction-diffusion equations, and I will explain some progress made in that direction for two types of continuous neural fields: the Amari-Wilson-Cowan equation and the nonlocal Nagumo equation.

Information about the video

Date of recording 03/02/2022
Date of publication 03/02/2022
Institution IHP
Language English
Audience Researchers
Director(s) Mandarine Audiovisuel
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2022.T1.WS2.023
Cite this video Faye, Grégory (03/02/2022). Front initiation in continuous neural fields. IHP. Audiovisual resource. DOI: 10.57987/IHP.2022.T1.WS2.023
URL https://dx.doi.org/10.57987/IHP.2022.T1.WS2.023

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