Waves, bumps, and patterns in neural field theories

被引:334
作者
Coombes, S [1 ]
机构
[1] Univ Nottingham, Dept Math Sci, Nottingham NG7 2RD, England
关键词
bumps; waves; neural field theories; integral equations; Evans functions;
D O I
10.1007/s00422-005-0574-y
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
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.
引用
收藏
页码:91 / 108
页数:18
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