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

P.M. Lima, W. Erlhagen, M.V. Kulikova and G.Yu. Kulikov

Physica A: Statistical Mechanics and its Applications, 2022, vol. 596, issue C

Abstract: 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.

Keywords: Stochastic neural field equation; Galerkin method; One- and multi-bump solutions (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:596:y:2022:i:c:s0378437122001741

DOI: 10.1016/j.physa.2022.127166

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