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

Coombes, Stephen; Owen, Markus R.



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.


Coombes, S., & Owen, M. R. (2005). Bumps, breathers, and waves in a neural network with spike frequency adaptation. Physical Review Letters, 94(14),

Journal Article Type Article
Publication Date Apr 15, 2005
Deposit Date Mar 7, 2005
Publicly Available Date Oct 9, 2007
Journal Physical Review Letters
Print ISSN 0031-9007
Electronic ISSN 1079-7114
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 94
Issue 14
Public URL
Publisher URL


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