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 tis- sue in mathematical neuroscience. Studying these models with a sigmoidal fir- ing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectiv- ities. 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 an 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.