Bumps, breathers, and waves in a neural network with spike frequency adaptation

Coombes, Stephen and Owen, Markus (2005) Bumps, breathers, and waves in a neural network with spike frequency adaptation.

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In this Letter we introduce a continuum model of neural tissue that include the effects of so-called spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon the non-local network connectivity, synaptic response, and firing rate of a single neuron. A phenomenological model of SFA is examined whereby the firing rate is taken to be a simple state-dependent threshold function. As in the case without SFA classical Mexican-Hat connectivity is shown to allow for the existence of spatially localized states (bumps). Importantly an analysis of bump stability using recent Evans function techniques shows that bumps may undergo instabilities leading to the emergence of both breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. Direct numerical simulations both confirm our theoretical predictions and illustrate the rich dynamic behavior of this model, including the appearance of self-replicating bumps.

Item Type: Article
Additional Information: To appear in Physical Review Letters
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Depositing User: Coombes, Prof Stephen
Date Deposited: 07 Mar 2005
Last Modified: 14 Sep 2016 03:51
URI: http://eprints.nottingham.ac.uk/id/eprint/149

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