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

• Autor(a) principal: Lima, P. M.
• Data de Publicação: 2022
• Outros Autores: Erlhagen, Wolfram, Kulikova, M.V., Kulikov, G.Yu.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: https://hdl.handle.net/1822/85432
• topic: Stochastic dynamic neural field; Galerkin method; Multi-bump solution; Working memory; Stochastic neural field equation; One-and multi-bump solutions; Ciências Naturais::Matemáticas; Science & Technology

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.