[Dynamique de réseaux de neurones inhomogènes structurés en âge]
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.
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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@article{CRMATH_2015__353_12_1111_0,
author = {Kang, Moon-Jin and Perthame, Beno{\^\i}t and Salort, Delphine},
title = {Dynamics of time elapsed inhomogeneous neuron network model},
journal = {Comptes Rendus. Math\'ematique},
pages = {1111--1115},
publisher = {Elsevier},
volume = {353},
number = {12},
year = {2015},
doi = {10.1016/j.crma.2015.09.029},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.09.029/}
}
TY - JOUR AU - Kang, Moon-Jin AU - Perthame, Benoît AU - Salort, Delphine TI - Dynamics of time elapsed inhomogeneous neuron network model JO - Comptes Rendus. Mathématique PY - 2015 SP - 1111 EP - 1115 VL - 353 IS - 12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.09.029/ DO - 10.1016/j.crma.2015.09.029 LA - en ID - CRMATH_2015__353_12_1111_0 ER -
%0 Journal Article %A Kang, Moon-Jin %A Perthame, Benoît %A Salort, Delphine %T Dynamics of time elapsed inhomogeneous neuron network model %J Comptes Rendus. Mathématique %D 2015 %P 1111-1115 %V 353 %N 12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.09.029/ %R 10.1016/j.crma.2015.09.029 %G en %F CRMATH_2015__353_12_1111_0
Kang, Moon-Jin; Perthame, Benoît; Salort, Delphine. Dynamics of time elapsed inhomogeneous neuron network model. Comptes Rendus. Mathématique, Tome 353 (2015) no. 12, pp. 1111-1115. doi : 10.1016/j.crma.2015.09.029. http://www.numdam.org/articles/10.1016/j.crma.2015.09.029/
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