Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 71, Issue 2, Pages 379-408Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100799423
Keywords
neural fields; synaptic depression; piecewise-smooth dynamics
Categories
Funding
- National Science Foundation [DMS-0813677]
- Royal Society Wolfson Foundation
- [KUK-C1-013-4]
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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.
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