Mathematical Modeling of Working Memory in the Presence of Random Disturbance using Neural Field Equations

¹ Centro de Matemática Computacional e Estocástica, Instituto Superior Técnico, University of Lisbon, PR-1049 001 Lisboa, Portugal
² Centro de Matemática, Universidade do Minho, PR-4710-057, Guimarães, Portugal

^* e-mail: plima@math.tenico.ulisboa.pt;
^** e-mail: wolfram.erlhagen@math.uminho.pt;
^*** e-mail: gennady.kulikov@tecnico.ulisboa.pt;
^**** e-mail: maria.kulikova@tecnico.ulisboa.pt

Published online: 26 April 2021

Abstract

In this paper, we describe a neural field model which explains how a population of cortical neurons may encode in its firing pattern simultaneously the nature and time of sequential stimulus events. Moreover, we investigate how noise-induced perturbations may affect the coding process. This is obtained by means of a two-dimensional neural field equation, where one dimension represents the nature of the event (for example, the color of a light signal) and the other represents the moment when the signal has occurred. The additive noise is represented by a Q-Wiener process. Some numerical experiments reported are carried out using a computational algorithm for two-dimensional stochastic neural field equations.