Comptes Rendus
no. 12
Partial differential equations
Dynamics of time elapsed inhomogeneous neuron network model

Presented by: Haïm Brézis

Moon-Jin Kang1; Benoît Perthame2; Delphine Salort3
1 Department of Mathematics, Texas University, Austin, United States
2 Sorbonne Universités, UPMC (Université Paris-6), UMR 7598, CNRS, INRIA, Laboratoire Jacques-Louis-Lions, France
3 Sorbone Universités, UPMC (Université Paris-6), UMR 7238, CNRS, Laboratoire de biologie computationnelle et quantitative, France
Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1111-1115.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2015.09.029

Moon-Jin Kang 1; Benoît Perthame 2; Delphine Salort 3

1 Department of Mathematics, Texas University, Austin, United States
2 Sorbonne Universités, UPMC (Université Paris-6), UMR 7598, CNRS, INRIA, Laboratoire Jacques-Louis-Lions, France
3 Sorbone Universités, UPMC (Université Paris-6), UMR 7238, CNRS, Laboratoire de biologie computationnelle et quantitative, France 
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Moon-Jin Kang; Benoît Perthame; Delphine Salort. Dynamics of time elapsed inhomogeneous neuron network model. Comptes Rendus. Mathématique, Volume 353 (2015) no. 12, pp. 1111-1115. doi : 10.1016/j.crma.2015.09.029. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.09.029/

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