Relaxation and self-sustained oscillations in the time elapsed neuron network model
type: Item
instance of: scholarly article
zbMATH Open document ID: 1278.82046
DOI: 10.1137/110847962
author: Khashayar Pakdaman
author: Ben{ôı}t Perthame
author: Delphine Salort
published in: SIAM Journal on Applied Mathematics
publication date: 2013-09-30T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.3014
Mathematics Subject Classification ID: 82C32
Mathematics Subject Classification ID: 92B25
Mathematics Subject Classification ID: 34C26
zbMATH DE Number: 6212915
zbMATH Keywords: neuron networks
zbMATH Keywords: desynchronization
zbMATH Keywords: self-sustained oscillations
Wikidata QID: Q60502767
MaRDI profile type: Publication
OpenAlex ID: W2004044411
arXiv ID: 1109.3014
title: Relaxation and self-sustained oscillations in the time elapsed neuron network model
review text: The time elapsed model for neural networks has been introduced and studied by the authors in a previous paper [Nonlinearity 23, No. 1, 55--75 (2010; Zbl 1267.35239)]. The aim here is a further discussion on the convergence to asynchronous states and the construction of explicit periodic solutions in case assembly does not converge to the asynchronous state. After a presentation of the time elapsed model, results on convergence are proved in the sections `Dynamics of ensembles of disconnected neurons' and `Asynchronous activity for connected neuronal assemblies'. The section `Synchronous periodic oscillations in neuronal assemblies' is devoted to the construction of periodic solutions. Simulation results are shown.
reviewed by: Claudia Simionescu-Badea
description: scientific article; zbMATH DE number 6212915