In a large variety of systems (biological, physical, social etc.), synchronization occurs when different oscillating objects tune their rhythm when they interact with each other. The different underlying network defining the connectivity properties among these objects drives the global dynamics in a complex fashion and affects the global degree of synchrony of the system. Here we study the impact of such types of different network architectures, such as Fully-Connected, Random, Regular ring lattice graph, Small-World and Scale-Free in the global dynamical activity of a system of coupled Kuramoto phase oscillators. We fix the external stimulation parameters and we measure the global degree of synchrony when different fractions of nodes receive stimulus. These nodes are chosen either randomly or based on their respective strong/weak connectivity properties (centrality, shortest path length and clustering coefficient). Our main finding is, that in Scale-Free and Random networks a sophisticated choice of nodes based on their eigenvector centrality and average shortest path length exhibits a systematic trend in achieving higher degree of synchrony. However, this trend does not occur when using the clustering coefficient as a criterion. For the other types of graphs considered, the choice of the stimulated nodes (randomly vs selectively using the aforementioned criteria) does not seem to have a noticeable effect.

翻译：在生物、物理、社会等众多系统中，当不同振荡体相互作用时，会通过调整自身节律实现同步。定义这些振荡体之间连接特性的底层网络以复杂方式驱动整体动力学，并影响系统的全局同步程度。本研究考察了全连接网络、随机网络、正则环形晶格网络、小世界网络和无标度网络等不同网络架构对耦合Kuramoto相位振子系统全局动力学活动的影响。我们固定外部刺激参数，测量不同比例的节点接受刺激时的全局同步程度。这些节点或随机选取，或依据其强弱连接特性（中心性、最短路径长度和聚类系数）选择。主要发现是：在无标度网络和随机网络中，基于特征向量中心性和平均最短路径长度的节点精细选择呈现出实现更高同步程度的系统趋势。然而，当使用聚类系数作为标准时并未出现此趋势。对于其他类型的图，被刺激节点的选择方式（随机选取与选择性使用上述标准）似乎未产生显著影响。