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Main Title: Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations
Author(s): Lang, Eva
Stannat, Wilhelm
Type: Article
Language Code: en
Abstract: Neural field equations are used to describe the spatio-temporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under the assumption that each population in the network is large, the activity is described in terms of a population average. The discrete network is then approximated by a continuum. In this article we make the two approximation steps explicit. Extending a model by Bressloff and Newby, we describe the evolution of the activity in a discrete network of finite populations by a Markov chain. In order to determine finite-size effects—deviations from the mean-field limit due to the finite size of the populations in the network—we analyze the fluctuations of this Markov chain and set up an approximating system of diffusion processes. We show that a well-posed stochastic neural field equation with a noise term accounting for finite-size effects on traveling wave solutions is obtained as the strong continuum limit.
Issue Date: 6-Jul-2017
Date Available: 10-Dec-2018
DDC Class: 510 Mathematik
Subject(s): neural field equations
discrete network
Markov chain
Sponsor/Funder: TU Berlin, Open-Access-Publikationsfonds – 2017
DFG, GRK 1845, Stochastische Analysis mit Anwendungen in Biologie, Finanzen und Physik
BMBF, 01GQ1001B, Verbundprojekt: Bernstein Zentrum für Computational Neuroscience, Berlin - "Präzision und Variabilität" - Teilprojekt B2, B3, B5, Professur und Nachwuchsgruppe
Journal Title: Journal of Mathematical Neuroscience
Publisher: SpringerOpen
Publisher Place: London
Volume: 7
Article Number: 5
Publisher DOI: 10.1186/s13408-017-0048-2
ISSN: 2190-8567
Appears in Collections:FG Mathematische Stochastik / Stochastische Prozesse in den Neurowissenschaften » Publications

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