Traveling pulses and wave propagation failure in inhomogeneous neural media
File(s)
Published version
Author(s)
Kilpatrick, Zachary P
Folias, Stefanos E
Bressloff, Paul C
Type
Journal Article
Abstract
We use averaging and homogenization theory to study the propagation of traveling pulses in an inhomogeneous excitable neural 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. We show how a spatially periodic modulation of homogeneous synaptic connections leads to an effective reduction in the speed of a traveling pulse. In the case of large amplitude modulations, the traveling pulse represents the envelope of a multibump solution, in which individual bumps are nonpropagating and transient. The appearance (disappearance) of bumps at the leading (trailing) edge of the pulse generates the coherent propagation of the pulse. Wave propagation failure occurs when activity is insufficient to maintain bumps at the leading edge.
Date Issued
2008-01
Date Acceptance
2007-10-05
Citation
SIAM Journal on Applied Dynamical Systems, 2008, 7 (1), pp.161-185
ISSN
1536-0040
Publisher
Society for Industrial and Applied Mathematics
Start Page
161
End Page
185
Journal / Book Title
SIAM Journal on Applied Dynamical Systems
Volume
7
Issue
1
Copyright Statement
Copyright © 2008 Society for Industrial and Applied Mathematics.
Identifier
http://dx.doi.org/10.1137/070699214
Publication Status
Published
Date Publish Online
2008-01-23