Waves, bumps, and patterns in neural field theories
 S. Coombes
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Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integrodifferential equations. Their nonlocal nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axodendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.
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 Title
 Waves, bumps, and patterns in neural field theories
 Journal

Biological Cybernetics
Volume 93, Issue 2 , pp 91108
 Cover Date
 20050801
 DOI
 10.1007/s004220050574y
 Print ISSN
 03401200
 Online ISSN
 14320770
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Bumps
 Waves
 Neural field theories
 Integral equations
 Evans functions
 Industry Sectors
 Authors

 S. Coombes ^{(1)}
 Author Affiliations

 1. Department of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK