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

Pedro M. Lima,Gennady Yu. Kulikov,Maria V. Kulikova,Wolfram Erlhagen

doi:10.1051/epjconf/202124801021

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.

Highlights

In recent years, significant progress has been made in understanding the brain electrodynamics using mathematical techniques
Neural field models represent the large-scale dynamics of spatially structured networks of neurons in terms of nonlinear integro-differential equations. Such models are becoming increasingly important for the interpretation of experimental data, including those obtained from EEG, fMRI and optical imaging [2]
Working memory (WM) defined as the ability to actively retain stimulus information over short periods of time is crucial for cognitive control of behavior

Summary

Introduction

Significant progress has been made in understanding the brain electrodynamics using mathematical techniques. Neural field models represent the large-scale dynamics of spatially structured networks of neurons in terms of nonlinear integro-differential equations. Such models are becoming increasingly important for the interpretation of experimental data, including those obtained from EEG, fMRI and optical imaging [2]. We test the robustness of a dynamic neural field model of serial order in the presence of additive noise in an experiment in which a sequence of color cues is presented. Increase their firing probability to the presentation of external stimuli [21] Consisting with this view, we assume that only at field positions receiving the traveling wave and the color input simultaneously, the combined input is strong enough to trigger the evolution of a bump. One bump evolves in response to the combined input (see Fig.5), which persists after all inputs have been switched off (see Fig. 6)

Working Memory Application

Numerical Algorithm

Numerical Results

Conclusion