Synchronization reveals correlation between oscillators on networks

TL;DR

This paper derives an analytical expression linking oscillator correlations to network topology in synchronization dynamics, proposing a new measure and revealing how network heterogeneity influences collective synchronization.

Contribution

It provides an analytic correlation expression for oscillators on networks and introduces a new synchronization measure applicable to complex network structures.

Findings

Correlation relates network topology to oscillator dynamics

Heterogeneous and smaller networks synchronize more closely

New community detection algorithm based on correlation

Abstract

The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from the fully synchronized regime. We have got the analytic expression of the dynamical correlation between pairs of oscillators that reveals the relation between the network dynamics and the underlying topology. Moreover, it also reveals the internal structure of networks that can be used as a new algorithm to detect community structures. Further, we have proposed a new measure about the synchronization in complex networks and scrutinize it in small-world and scale-free networks. Our results indicate that the more heterogeneous and "smaller" the network is, the more closely it would be synchronized by the collective dynamics.