Navas A, Villacorta-Atienza J A, Leyva I, Almendral J A, Sendiña-Nadal I, Boccaletti S
Center for Biomedical Technology, Univ. Politécnica de Madrid, 28223 Pozuelo de Alarcón, Madrid, Spain.
Department of Applied Mathematics, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062820. doi: 10.1103/PhysRevE.92.062820. Epub 2015 Dec 15.
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. 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 effective centrality, a measure that quantifies the role and importance of each network's node in the synchronization process. In particular, in the context of explosive synchronization, we use such a measure to assess the propensity of a graph to sustain an irreversible transition to synchronization. We furthermore discuss a strategy to induce the explosive behavior in a generic network, by acting only upon a fraction of its nodes.
众所周知，网络振荡器的同步从根本上取决于图单元的动力学与网络结构的微观排列之间的相互作用。我们在此提出一种有效网络，其拓扑特性反映了原始网络的拓扑与动力学之间的相互作用。在此基础上，我们能够引入有效中心性，这是一种量化每个网络节点在同步过程中的作用和重要性的度量。特别是，在爆发性同步的背景下，我们使用这种度量来评估图维持向同步的不可逆转变的倾向。我们还讨论了一种仅通过作用于网络的一小部分节点来在一般网络中诱导爆发性行为的策略。
