Wave-front solution behaviour for continuous neural networks with lateral inhibition

Abstract

In this paper we discuss the shape of travelling wave-front solutions to a model for a single continuous layer of nerve cells originally introduced by Amari (1977, Dynamics of pattern formation in lateral inhibition-type neural fields. Biol. Cybern., 27, 77-87).The neural field is homogeneous and isotropic, and the connection function is one of lateral inhibition type, meaning that nearby connecting cells have an excitatory influence, while more spatially distant cells impose an inhibitory influence. We give results on the shape of the wave-front solutions, which are non-monotone and exhibit different shapes depending on the size of a threshold parameter. For a layer of excitatory cells indirectly inhibited by a second layer of cells, we derive results on the qualitative behaviour of wave-fronts for changes in parameters representing the inhibitory firing threshold and the time-scale of the inhibition process. This study shows how intrinsic cell and network parameter can interact to shape global response properties. © 2006 Oxford University Press.