Waves, bumps, and patterns in neural field theories

Coombes, Stephen

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.

Citation

Coombes, S. (2005). Waves, bumps, and patterns in neural field theories

• Journal Article Type: Article
• Publication Date: Mar 1, 2005
• Deposit Date: Apr 14, 2005
• Publicly Available Date: Oct 9, 2007
• Peer Reviewed: Peer Reviewed
• Keywords: bumps, waves, neural field theories, integral equations, Evans functions
• Public URL: http://eprints.nottingham.ac.uk/id/eprint/153
• Additional Information: To appear in Biological Cybernetics