numerical simulation of the stochastic neural field equation with delay

The neural field equations (nfe) are used to model the synaptic interactionsbetween neurons in a continuous neural network, called a neural eld. this kind ofintegro-dierential equations proved to be an useful tool to describe the spatiotemporalneural activity from a macroscopic point of view, allowing the study of a wide varietyof neurobiological phenomena, such as the sensory stimuli processing.the present article aims to study the eects of additive noise in one- and twodimensionalneuronal elds, while taking into account nite axonal velocity and externalstimulus. a galerkin-type method is presented, which applies fast fourier transformsto optimise the computational eort required to solve these equations. the expliciteuler-maruyama scheme is implemented to obtain the stochastic numerical solution.a published numerical solver written in julia is used to simulate the neural elds instudy.