Two-dimensional bumps in piecewise smooth neural fields with synaptic depression
File(s)
Published version
Author(s)
Bressloff, Paul C
Kilpatrick, Zachary P
Type
Journal Article
Abstract
We analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Synaptic depression dynamically reduces the strength of synaptic weights in response to increases in activity. We show that in the case of a Mexican hat weight distribution, sufficiently strong synaptic depression can destabilize a stationary bump solution that would be stable in the absence of depression. Numerically it is found that the resulting instability leads to the formation of a traveling spot. The local stability of a bump is determined by solutions to a system of pseudolinear equations that take into account the sign of perturbations around the circular bump boundary.
Date Issued
2011-01
Date Acceptance
2010-12-07
Citation
SIAM Journal on Applied Mathematics, 2011, 71 (2), pp.379-408
ISSN
0036-1399
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Start Page
379
End Page
408
Journal / Book Title
SIAM Journal on Applied Mathematics
Volume
71
Issue
2
Copyright Statement
Copyright © 2011 Society for Industrial and Applied Mathematics.
Identifier
http://dx.doi.org/10.1137/100799423
Publication Status
Published
Date Publish Online
2011-03-03