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

^** Email: rsittipong{at}yahoo.com^*** Corresponding author. Email: jbell{at}math.umbc.edu^**** Email: scylb{at}mahidol.ac.th In this paper we discuss the shape of travelling wave-frontsolutions to a model for a single continuous layer of nervecells originally introduced by Amari (1977, Dynamics of patternformation 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, whichare non-monotone and exhibit different shapes depending on thesize of a threshold parameter. For a layer of excitatory cellsindirectly inhibited by a second layer of cells, we derive resultson the qualitative behaviour of wave-fronts for changes in parametersrepresenting the inhibitory firing threshold and the time-scaleof the inhibition process. This study shows how intrinsic celland network parameter can interact to shape global responseproperties.