Stability in a scalar differential equation with multiple, distributed time delays

TL;DR

This paper investigates the stability of a scalar delay differential equation with two distributed delays, providing conditions for stability that are independent of delay distributions and explicitly describing stability regions for specific cases.

Contribution

It introduces necessary stability conditions for scalar DDEs with multiple distributed delays, including explicit stability regions for gamma distributed delays.

Findings

Necessary stability conditions independent of delay distributions

Explicit stability region for one discrete and one gamma distributed delay

Analysis of how stability depends on model parameters

Abstract

We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the case of one discrete and one gamma distributed delay, we give an explicit description of the region of stability of the trivial solution and discuss how this depends on the model parameters.