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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
10/2001

Nonlinear analysis of spatio-temporal receptive fields: I. Dynamic approximation method

Thomas Wennekers

Abstract

I present an approximation method that reduces the spatio-temporal dynamics of localized solutions of nonlinear neural field equations ("bumps") to a set of ordinary differential equations for just the amplitudes and tuning widths of the activation peaks. This enables a practicable analysis of spatio-temporal point spread functions, steady state receptive field profiles, and their stability properties. The lowest order approximation for the amplitudes alone is equivalent to meanfield equations for homogeneously coupled pools of Poissonian neurons. Thus, much of the well studied meanfield behavior should carry over to localized solutions in neural fields.

Received:
Feb 27, 2001
Published:
Feb 27, 2001
Keywords:
receptive fields, neural field equations, nonlinear approximation

Related publications

inJournal
2002 Repository Open Access
Thomas Wennekers

Nonlinear analysis of spatio-temporal receptive fields: I. Dynamic approximation method

In: Neurocomputing, 44 (2002), pp. 201-206