Neural fields with sigmoidal firing rates: approximate solutions

Coombes, Stephen and Schmidt, Helmut (2010) Neural fields with sigmoidal firing rates: approximate solutions. Discrete and Continuous Dynamical Systems. Series S . ISSN 1937-1632 (Submitted)

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Official URL: http://www.aimsciences.org/journals/dcdsS/index.htm

Abstract

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for stationary and travelling wave solutions, that can deal with a certain class of smoothed Heaviside functions. The distribution that smoothes the Heaviside is viewed as a fundamental object, and all expressions describing the scheme are constructed in terms of integrals over this distribution. The comparison of our scheme and results from direct numerical simulations is used to highlight the very good levels of approximation that can be achieved by iterating the process only a small number of times.

Item Type:Article
Uncontrolled Keywords:integro-differential equations neural field models sigmoidal firing rate approximation theory
Schools/Departments:Faculty of Science > School of Mathematical Sciences
ID Code:1233
Deposited By:Coombes, Prof Stephen
Deposited On:23 Feb 2010 10:13
Last Modified:23 Jun 2011 07:52

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