Speed of complex network synchronization

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.

14 pages, 7 figures, accepted for publication in EPJB, epj style, v2: typos corrected

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Cited by in corpus (10)

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• Collective Relaxation Dynamics of Small-World Networks
• Small-world spectra in mean field theory
• Recovery time after localized perturbations in complex dynamical networks
• Relaxation time of the global order parameter on multiplex networks: the role of interlayer coupling in Kuramoto oscillators
• Influence of cumulative damage on synchronization of Kuramoto oscillators on networks
• Antifragility and response to damage in the synchronization of oscillators on networks
• Notes on Resonant and Synchronized States in Complex Networks
• Consensus on Moving Neighborhood Model of Peterson Graph
• Controlling synchronization in coupled area-preserving maps using stickiness