Numerical Simulations in Two-Dimensional Neural Fields

TL;DR

This paper develops and tests a numerical algorithm for approximating two-dimensional neural field equations with delay, validating it against known examples and analyzing solution properties for real-world relevance.

Contribution

It introduces a numerical algorithm for delayed neural field equations and provides detailed analysis and validation against existing solutions.

Findings

The algorithm accurately approximates known neural field solutions.

Numerical results align well with previous studies.

Analysis offers insights into the physical interpretation of solutions.

Abstract

In the present paper we are concerned with a numerical algorithm for the approximation of the two-dimensional neural field equation with delay. We consider three numerical examples that have been analysed before by other authors and are directly connected with real world applications. The main purposes are 1) to test the performance of the mentioned algorithm, by comparing the numerical results with those obtained by other authors; 2) to analyse with more detail the properties of the solutions and take conclusions about their physical meaning.