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Waves, bumps, and patterns in neural field theories

Coombes, Stephen

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Abstract

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 integro-differential equations. Their non-local 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 axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.

Journal Article Type Article
Publication Date Mar 1, 2005
Peer Reviewed Peer Reviewed
APA6 Citation Coombes, S. (2005). Waves, bumps, and patterns in neural field theories
Keywords bumps, waves, neural field theories, integral equations, Evans functions
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information To appear in Biological Cybernetics

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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