Synchronization of an Excitatory Integrate-and-Fire Neural Network

Grégory Dumont 1, 2 Jacques Henry 1, 2
2 CARMEN - Modélisation et calculs pour l'électrophysiologie cardiaque
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest, IHU-LIRYC
Abstract : In this paper, we study the influence of the coupling strength on the synchronization behavior of a population of leaky integrate-and-fire neurons that is selfexcitatory with a population density approach. Each neuron of the population is assumed to be stochastically driven by an independent Poisson spike train and the synaptic interaction between neurons is modeled by a potential jump at the reception of an action potential. Neglecting the synaptic delay, we will establish that for a strong enough connectivity between neurons, the solution of the partial differential equation which describes the population density function must blow up in finite time. Furthermore, we will give a mathematical estimate on the average connection per neuron to ensure the occurrence of a burst. Interpreting the blow up of the solution as the presence of a Dirac mass in the firing rate of the population, we will relate the blow up of the solution to the occurrence of the synchronization of neurons. Fully stochastic simulations of a finite size network of leaky integrate-and-fire neurons are performed to illustrate our theoretical results.
Type de document :
Article dans une revue
Bulletin of Mathematical Biology, Springer Verlag, 2013, 75 (4), pp.629-648. 〈10.1007/s11538-013-9823-8〉
Liste complète des métadonnées

Littérature citée [25 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/hal-00822472
Contributeur : Jacques Henry <>
Soumis le : mardi 14 mai 2013 - 17:02:50
Dernière modification le : jeudi 11 janvier 2018 - 06:23:41
Document(s) archivé(s) le : lundi 19 août 2013 - 16:05:10

Fichier

explosion-revised.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Grégory Dumont, Jacques Henry. Synchronization of an Excitatory Integrate-and-Fire Neural Network. Bulletin of Mathematical Biology, Springer Verlag, 2013, 75 (4), pp.629-648. 〈10.1007/s11538-013-9823-8〉. 〈hal-00822472〉

Partager

Métriques

Consultations de la notice

333

Téléchargements de fichiers

197