Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression
KAUST Grant NumberKUK-C1-013-4
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AbstractWe 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. © 2011 Society for Industrial and Applied Mathematics.
CitationBressloff PC, Kilpatrick ZP (2011) Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression. SIAM Journal on Applied Mathematics 71: 379–408. Available: http://dx.doi.org/10.1137/100799423.
SponsorsThis publication was based on work supported in partby the National Science Foundation (DMS-0813677) and by award KUK-C1-013-4 made by KingAbdullah University of Science and Technology (KAUST).