Numerical solution of the stochastic neural field equation with applications to working memory

The main goal of the present work is to investigate the effect of noise in some neural fields, used to simulate working memory processes. The underlying mathematical model is a stochastic integro-differential equation. In order to approximate this equation we apply a numerical scheme which uses the Galerkin method for the space discretization. In this way we obtain a system of stochastic differential equations, which are then approximated in two different ways, using the Euler–Maruyama and the Itô–Taylor methods. We apply this numerical scheme to explain how a population of cortical neurons may encode in its firing pattern simultaneously the nature and time of sequential stimulus events. Numerical examples are presented and their results are discussed.The authors acknowledge the financial support of the Portuguese FCT (Fundacao para a Ciencia e Tecnologia), Portugal, through projects UIDB/04621/2020, UIDP/04621/2020 (IST), UIDB/00013/2020, UIDP/00013/2020 (UMinho) and PTDC/MAT-APL/31393/2017. The authors are also grateful to the reviewers for their careful reading of the text and helpful suggestions that contributed to the improvement of the article