Stability of networks of delay-coupled delay oscillators

TL;DR

This paper extends generalized modeling to analyze the stability of large networks of delay-coupled delay oscillators, revealing patterns of stability and conditions where topology perturbations significantly impact network stability.

Contribution

It introduces a novel approach linking structure and dynamics to assess stability in large delay-coupled networks, including conditions for topology perturbation effects.

Findings

Pattern of stability tongues as delays vary

Topology perturbations can strongly affect stability

Analytical approximation of stability in large networks

Abstract

Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When the local dynamical stability of the network is plotted as a function of the two delays then a pattern of tongues is revealed. Exploiting a link between structure and dynamics, we identify conditions under which perturbations of the topology have a strong impact on the stability. If these critical regions are avoided the local stability of large random networks can be well approximated analytically.