Bumps in simple two-dimensional neural field models

Olivier Faugeras 1 François Grimbert 1, *
* Auteur correspondant
1 ODYSSEE - Computer and biological vision
DI-ENS - Département d'informatique de l'École normale supérieure, CRISAM - Inria Sophia Antipolis - Méditerranée , ENS Paris - École normale supérieure - Paris, Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : Neural field models first appeared in the 50's, but the theory really took off in the 70's with the works of Wilson and Cowan {wilson-cowan:72,wilson-cowan:73} and Amari {amari:75,amari:77}. Neural fields are continuous networks of interacting neural masses, describing the dynamics of the cortical tissue at the population level. In this report, we study homogeneous stationary solutions (i.e independent of the spatial variable) and bump stationary solutions (i.e. localized areas of high activity) in two kinds of infinite two-dimensional neural field models composed of two neuronal layers (excitatory and inhibitory neurons). We particularly focus on bump patterns, which have been observed in the prefrontal cortex and are involved in working memory tasks {goldman-rakic:95}. We first show how to derive neural field equations from the spatialization of mesoscopic cortical column models. Then, we introduce classical techniques borrowed from Coombes {coombes:05} and Folias and Bressloff {folias-bressloff:04} to express bump solutions in a closed form and make their stability analysis. Finally we instantiate these techniques to construct stable two-dimensional bump solutions.
Type de document :
Rapport
[Research Report] RR-6375, INRIA. 2007, pp.19
Liste complète des métadonnées

Littérature citée [15 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00192952
Contributeur : François Grimbert <>
Soumis le : jeudi 17 janvier 2008 - 09:23:14
Dernière modification le : mardi 17 avril 2018 - 11:33:26
Document(s) archivé(s) le : jeudi 23 septembre 2010 - 16:29:38

Fichier

RR-6375.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : inria-00192952, version 3

Collections

Citation

Olivier Faugeras, François Grimbert. Bumps in simple two-dimensional neural field models. [Research Report] RR-6375, INRIA. 2007, pp.19. 〈inria-00192952v3〉

Partager

Métriques

Consultations de la notice

378

Téléchargements de fichiers

97