A numerical scheme for the one-dimensional neural field model

Abstract

Neural field models, typically cast as continuum integro-differential equations, are widely studied to describe the coarse-grained dynamics of real cortical tissue in mathematical neuroscience. Studying these models with a sigmoidal firing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectivities. Because of the convolution structure of these integrals, it is possible to evaluate neural field model using a pseudo-spectral method, where Fourier Transform (FT) followed by an inverse Fourier Transform (IFT) is performed, leading to a new identical partial differential equation. In this paper, we revisit a neural field model with a nonlinear sigmoidal firing rate and provide an efficient numerical algorithm to analyse the model regarding finite volume scheme. On the other hand, numerical results are obtained by the algorithm.