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Comptes Rendus Mathématique
Volume 353, n° 12
pages 1111-1115 (décembre 2015)
Doi : 10.1016/j.crma.2015.09.029
Received : 28 September 2015 ;  accepted : 30 September 2015
Dynamics of time elapsed inhomogeneous neuron network model
Dynamique de réseaux de neurones inhomogènes structurés en âge
 

Moon-Jin Kang a , Benoît Perthame b , Delphine Salort c
a Department of Mathematics, Texas University, Austin, United States 
b Sorbonne Universités, UPMC (Université Paris-6), UMR 7598, CNRS, INRIA, Laboratoire Jacques-Louis-Lions, France 
c Sorbone Universités, UPMC (Université Paris-6), UMR 7238, CNRS, Laboratoire de biologie computationnelle et quantitative, France 

Abstract

Models for neural networks have been proposed, which describe the probability to find a neuron for which time s has elapsed since the last discharge. These are written under the form of a nonlinear age-structured equation where the total network activity modulates the firing rate. Here, we consider an inhomogeneous network with variability on the refractory period. We give conditions on the connectivity, leading to total desynchronization of the network.

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Résumé

Pour décrire l'activité de réseaux de neurones, des modèles qui représentent la probabilité qu'un neurone ait passé le temps s depuis sa dernière décharge ont été proposés. Ce sont des équations structurées en âge, non linéaires, où l'activité totale du réseau contrôle le taux de décharge. Ici, nous considérons un réseau inhomogène prenant en compte la variabilité des périodes réfractaires. Nous donnons une condition sur la connectivité qui conduit à la désynchronisation totale.

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