Synchronization centrality and explosive synchronization in complex networks

TL;DR

This paper introduces a new measure called synchronization centrality that quantifies node importance in network synchronization and predicts explosive synchronization phenomena, providing insights and strategies to induce such behavior.

Contribution

It proposes an effective network model and the synchronization centrality measure, linking network topology and dynamics to explain and control explosive synchronization.

Findings

Synchronization centrality predicts explosive synchronization.

The measure identifies key nodes influencing synchronization.

A strategy to induce explosive synchronization by targeting few nodes.

Abstract

Synchronization of networked oscillators is known to depend fundamentally on the interplay between the dynamics of the graph's units and the microscopic arrangement of the network's structure. For non identical elements, the lack of quantitative tools has hampered so far a systematic study of the mechanisms behind such a collective behavior. We here propose an effective network whose topological properties reflect the interplay between the topology and dynamics of the original network. On that basis, we are able to introduce the "synchronization centrality", a measure which quantifies the role and importance of each network's node in the synchronization process. In particular, we use such a measure to assess the propensity of a graph to synchronize explosively, thus indicating a unified framework for most of the different models proposed so far for such an irreversible transition. Taking advantage of the predicting power of this measure, we furthermore discuss a strategy to induce the explosive behavior in a generic network, by acting only upon a small fraction of its nodes.