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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.
