Synchronization centrality and explosive synchronization in complex networks

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.

References in corpus (8)

• Synchronization in complex networks
• Critical phenomena in complex networks
• Explosive Synchronization Transitions in Scale-free Networks
• Explosive synchronization in adaptive and multilayer networks
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Explosive first-order transition to synchrony in networked chaotic oscillators
• From Scale-free to Erdos-Renyi Networks
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Cited by in corpus (8)

• The Kuramoto model in complex networks
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Explosive Phenomena in Complex Networks
• Emergent explosive synchronization in adaptive complex networks
• Dynamical complexity as a proxy for the network degree distribution
• Statistical complexity and connectivity relationship in cultured neural networks
• Explosive synchronization transition in a ring of coupled oscillators
• Characterizing correlations and synchronization in collective dynamics