Weakly interacting pulses in synaptically coupled neural media
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Published version
Author(s)
Bressloff, PC
Type
Journal Article
Abstract
We use singular perturbation theory to analyze the dynamics of N weakly interacting pulses in a one-dimensional synaptically coupled neuronal network. The network is modeled in terms of a nonlocal integro-differential equation, in which the integral kernel represents the spatial distribution of synaptic weights, and the output activity of a neuron is taken to be a mean firing rate. We derive a set of N coupled ordinary differential equations (ODEs) for the dynamics of individual pulses, establishing a direct relationship between the explicit form of the pulse interactions and the structure of the long-range synaptic coupling. The system of ODEs is used to explore the existence and stability of stationary N-pulses and traveling wave trains.
Date Issued
2005-01
Date Acceptance
2005-04-13
ISSN
0036-1399
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Start Page
57
End Page
81
Journal / Book Title
SIAM Journal on Applied Mathematics
Volume
66
Issue
1
Copyright Statement
Copyright © 2005 Society for Industrial and Applied Mathematics.
Identifier
http://dx.doi.org/10.1137/040616371
Publication Status
Published
Date Publish Online
2005-10-03