Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis

Grégory Faye 1 James Rankin 1 Pascal Chossat 2
1 NEUROMATHCOMP
CRISAM - Inria Sophia Antipolis - Méditerranée , INRIA Rocquencourt, ENS Paris - École normale supérieure - Paris, UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : The existence of spatially localized solutions in neural networks is an important topic in neuroscience as these solutions are considered to characterize working (short-term) memory. We work with an unbounded neural network represented by the neural field equation with smooth firing rate function and a wizard hat spatial connectivity. Noting that stationary solutions of our neural field equation are equivalent to homoclinic orbits in a related fourth order ordinary differential equation, we apply normal form theory for a reversible Hopf bifurcation to prove the existence of localized solutions; further, we present results concerning their stability. Numerical continuation is used to compute branches of localized solution that exhibit snaking-type behaviour. We describe in terms of three parameters the exact regions for which localized solutions persist.
Type de document :
Rapport
[Research Report] RR-7872, INRIA. 2012, pp.31
Liste complète des métadonnées

https://hal.inria.fr/hal-00665464
Contributeur : Grégory Faye <>
Soumis le : jeudi 2 février 2012 - 09:12:07
Dernière modification le : jeudi 26 avril 2018 - 10:28:52
Document(s) archivé(s) le : lundi 19 novembre 2012 - 15:40:32

Fichier

RR-7872.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00665464, version 1

Citation

Grégory Faye, James Rankin, Pascal Chossat. Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis. [Research Report] RR-7872, INRIA. 2012, pp.31. 〈hal-00665464〉

Partager

Métriques

Consultations de la notice

410

Téléchargements de fichiers

134