Synchronizability of networks with strongly delayed links: A universal classification

TL;DR

This paper demonstrates that for large delays, the synchronizability of delay-coupled networks depends on spectral properties and exhibits a universal structure in the master stability function, enabling a classification of networks based on their synchronization ability.

Contribution

It introduces a universal structure of the master stability function for large delays and provides a classification scheme for network synchronizability based on spectral properties.

Findings

Master stability function becomes rotationally symmetric at large delays

Synchronization stability relates to spectral properties of network topology

Universal classification scheme for network synchronizability

Abstract

We show that for large coupling delays the synchronizability of delay-coupled networks of identical units relates in a simple way to the spectral properties of the network topology. The master stability function used to determine stability of synchronous solutions has a universal structure in the limit of large delay: it is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. We give details of the proof of this structure and discuss the resulting universal classification of networks with respect to their synchronization properties. We illustrate this classification by means of several prototype network topologies.