Speed of complex network synchronization

TL;DR

This paper investigates how the topology of directed networks influences the speed of synchronization, revealing that increased randomness generally accelerates convergence, with specific effects observed in small-world regimes.

Contribution

It extends the Master Stability Function approach to quantify synchronization times across various network topologies, including real-world networks.

Findings

Stronger topological randomness leads to faster synchronization at fixed in-degree.

Synchronization is slowest at intermediate randomness in small-world networks.

Real-world networks confirm the topology-dependent synchronization times.

Abstract

Synchrony is one of the most common dynamical states emerging on networks. The speed of convergence towards synchrony provides a fundamental collective time scale for synchronizing systems. Here we study the asymptotic synchronization times for directed networks with topologies ranging from completely ordered, grid-like, to completely disordered, random, including intermediate, partially disordered topologies. We extend the approach of Master Stability Functions to quantify synchronization times. We find that the synchronization times strongly and systematically depend on the network topology. In particular, at fixed in-degree, stronger topological randomness induces faster synchronization, whereas at fixed path length, synchronization is slowest for intermediate randomness in the small-world regime. Randomly rewiring real-world neural, social and transport networks confirms this picture.