The Effects of Structural Perturbations on the Synchronizability of Diffusive Networks

TL;DR

This paper studies how structural changes in diffusive networks, including adding directed links, affect their ability to synchronize, providing classifications and conditions that either hinder or enhance synchronizability.

Contribution

It introduces a classification of directed links based on their impact on synchronizability and identifies conditions under which network perturbations can improve or impair synchronization.

Findings

Adding directed links can hinder or enhance synchronizability.

Networks can be made strongly connected while either hindering or improving synchronization.

Existence of specific perturbations that increase synchronizability by adding a single link.

Abstract

We investigate the effects of structural perturbations of both, undirected and directed diffusive networks on their ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directed links in weakly connected networks having a strongly connected component acting as driver. When the connectivity of the driver is not stronger than the connectivity of the slave component, we can always make the network strongly connected while hindering synchronization. On the other hand, we prove the existence of a perturbation which makes the network strongly connected while increasing the synchronizability. Under additional conditions, there is a node in the driving component such that adding a single link starting at an arbitrary node of the driven component and ending at this node increases the synchronizability.