Enhancing complex-network synchronization

TL;DR

This paper identifies conditions under which directed, weighted networks can achieve enhanced synchronization, making synchronizability depend only on average degree and reducing coupling costs, especially in scale-free networks.

Contribution

It uncovers a condition for improved synchronization in directed weighted networks, showing that synchronizability can be optimized independently of network size and degree distribution details.

Findings

Synchronizability depends solely on average degree in the optimal regime.

Weighted directed networks can drastically improve synchronization in scale-free networks.

Network coupling costs are significantly reduced with weighted coupling.

Abstract

Heterogeneity in the degree (connectivity) distribution has been shown to suppress synchronization in networks of symmetrically coupled oscillators with uniform coupling strength (unweighted coupling). Here we uncover a condition for enhanced synchronization in directed networks with weighted coupling. We show that, in the optimum regime, synchronizability is solely determined by the average degree and does not depend on the system size and the details of the degree distribution. In scale-free networks, where the average degree may increase with heterogeneity, synchronizability is drastically enhanced and may become positively correlated with heterogeneity, while the overall cost involved in the network coupling is significantly reduced as compared to the case of unweighted coupling.