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    Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression

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    Type
    Article
    Authors
    Bressloff, Paul C.
    Kilpatrick, Zachary P.
    KAUST Grant Number
    KUK-C1-013-4
    Date
    2011-01
    Permanent link to this record
    http://hdl.handle.net/10754/599851
    
    Metadata
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    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. © 2011 Society for Industrial and Applied Mathematics.
    Citation
    Bressloff 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.
    Sponsors
    This 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).
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Applied Mathematics
    DOI
    10.1137/100799423
    ae974a485f413a2113503eed53cd6c53
    10.1137/100799423
    Scopus Count
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