The Effects of Structural Perturbations on the Synchronizability of Diffusive Networks

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.

References in corpus (8)

• Synchronization in small-world systems
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Spontaneous synchrony in power-grid networks
• Network Synchronization, Diffusion, and the Paradox of Heterogeneity
• Synchronization is optimal in non-diagonalizable networks
• The Matrix of Maximum Out Forests of a Digraph and Its Applications
• Hub Synchronization in Scale-Free Networks
• The Fiedler Rose: On the extreme points of the Fiedler vector