Can distributed delays perfectly stabilize dynamical networks?

TL;DR

This paper investigates how different distributions of signal delays affect the stability of neural networks, revealing conditions under which delays stabilize or destabilize the system.

Contribution

It provides a mathematical analysis of neural network stability under various distributed delay conditions, highlighting the stabilizing effects of highly dispersed delays.

Findings

Gamma distributed delays can cause reentrant stability phenomena.

Highly dispersed delays prevent destabilization.

Delay dispersion influences neural network stability.

Abstract

Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integro-differential equation that describes the collective dynamics of a neural network with distributed signal delays. With the gamma distributed delays less dispersed than exponential distribution, the system exhibits reentrant phenomena, in which the stability is once lost but then recovered as the mean delay is increased. With delays dispersed more highly than exponential, the system never destabilizes.