Weighted networks are more synchronizable: how and why

TL;DR

This paper investigates how combining weight and degree heterogeneities in weighted networks enhances synchronization, providing theoretical insights and extending findings to phase synchronization in non-identical systems.

Contribution

It demonstrates that appropriate weighting schemes can significantly improve network synchronizability, overcoming the suppressive effects of heterogeneity.

Findings

Weighted networks synchronize more effectively when weights and degrees are optimally combined.

Synchronization becomes independent of heterogeneity distributions under certain weighting conditions.

The analysis extends to phase synchronization in networks of non-identical dynamical units.

Abstract

Most real-world networks display not only a heterogeneous distribution of degrees, but also a heterogeneous distribution of weights in the strengths of the connections. Each of these heterogeneities alone has been shown to suppress synchronization in random networks of dynamical systems. Here we review our recent findings that complete synchronization is significantly enhanced and becomes independent of both distributions when the distribution of weights is suitably combined with the distribution of degrees. We also present new results addressing the optimality of our findings and extending our analysis to phase synchronization in networks of non-identical dynamical units.