Existence of an equilibrium for delayed neural fields under output proportional feedback

TL;DR

This paper establishes that bounded activation functions ensure the existence of equilibrium points in delayed neural fields under output proportional feedback, extending stability analysis in neural network models.

Contribution

It provides a sufficient condition for equilibrium existence in delayed neural fields with output feedback, based on bounded activation functions.

Findings

Bounded activation functions guarantee equilibrium existence.

Equilibrium existence is linked to the stability of the neural field system.

The results extend previous stability conditions for neural networks.

Abstract

Recently, [2] proved that the closed-loop system resulting from the output proportional feedback stabilization of a class of delayed neural fields is input-to-state stable (ISS) for sufficiently high gain, subject to the existence of an equilibrium point for the closed-loop system. In the present paper, we show that a sufficient condition for such an equilibrium to exist is that the activation functions are bounded.