Bumps, Breathers, and Waves in a Neural Network with Spike Frequency Adaptation

S. Coombes and M. R. Owen
Phys. Rev. Lett. 94, 148102 – Published 14 April 2005

Abstract

We introduce a continuum model of neural tissue that includes the effects of spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon nonlocal network connectivity, synaptic response, and the firing rate of a single neuron. We consider a phenomenological model of SFA via a simple state-dependent threshold firing rate function. As without SFA, Mexican-hat connectivity allows for the existence of spatially localized states (bumps). Importantly recent Evans function techniques are used to show that bumps may destabilize leading to the emergence of breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. Simulations confirm our theoretical predictions and illustrate the rich behavior of this model.

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  • Received 28 November 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.148102

©2005 American Physical Society

Authors & Affiliations

S. Coombes and M. R. Owen

  • School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, United Kingdom

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Vol. 94, Iss. 14 — 15 April 2005

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