Symmetries and cluster synchronization in multilayer networks
Symmetries and cluster synchronization in multilayer networks
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DOI：
10.1038/s41467-020-16343-0
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发表时间：
2020-06-23
影响因子：
16.6
通讯作者：
Sorrentino, Francesco
中科院分区：
文献类型：
--
作者：
Della Rossa, Fabio;Pecora, Louis;Sorrentino, Francesco
流行病学、社会科学、电力运输、经济学和工程学中的现实系统通常被描述为多层网络。本文首先定义并计算了多层网络的对称性，然后研究了这些网络中集群同步的出现。我们区分了独立层对称和依赖层对称，前者发生在一层中，独立于其他层，后者涉及不同层中的节点。我们通过将问题解耦为多个独立的块，并通过主稳定性函数评估每个块的稳定性来研究集群同步解的稳定性。我们看到与依赖层对称相关的块与其他块具有不同的结构，这影响了与这些对称相关的簇的稳定性。最后，我们在一个全模拟实验中验证了这一理论，其中七个三种电子振荡器与两种耦合连接。现实世界中的复杂系统通常以多种方式相互作用的连接模式为特征。在这里，Della Rossa等人描述了一种确定多层网络对称性的一般方法，然后将其与网络可能表现出的不同同步模式联系起来。
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the emergence of cluster synchronization in these networks. We distinguish between independent layer symmetries, which occur in one layer and are independent of the other layers, and dependent layer symmetries, which involve nodes in different layers. We study stability of the cluster synchronous solution by decoupling the problem into a number of independent blocks and assessing stability of each block through a Master Stability Function. We see that blocks associated with dependent layer symmetries have a different structure to the other blocks, which affects the stability of clusters associated with these symmetries. Finally, we validate the theory in a fully analog experiment in which seven electronic oscillators of three kinds are connected with two kinds of coupling. Complex systems in the real world are often characterized by connected patterns interacting between each other in multiple ways. Here, Della Rossa et al. describe a general method to determine symmetries in multilayer networks and then relate them to different synchronization modes that the networks can exhibit.