DITEN, University of Genoa, Genova, Italy.
Mechanical Engineering Department, University of New Mexico, Albuquerque, NM, USA.
Nat Commun. 2021 Jul 1;12(1):4073. doi: 10.1038/s41467-021-24363-7.
Cluster synchronization in networks of coupled oscillators is the subject of broad interest from the scientific community, with applications ranging from neural to social and animal networks and technological systems. Most of these networks are directed, with flows of information or energy that propagate unidirectionally from given nodes to other nodes. Nevertheless, most of the work on cluster synchronization has focused on undirected networks. Here we characterize cluster synchronization in general directed networks. Our first observation is that, in directed networks, a cluster A of nodes might be one-way dependent on another cluster B: in this case, A may remain synchronized provided that B is stable, but the opposite does not hold. The main contribution of this paper is a method to transform the cluster stability problem in an irreducible form. In this way, we decompose the original problem into subproblems of the lowest dimension, which allows us to immediately detect inter-dependencies among clusters. We apply our analysis to two examples of interest, a human network of violin players executing a musical piece for which directed interactions may be either activated or deactivated by the musicians, and a multilayer neural network with directed layer-to-layer connections.
网络中耦合振子的簇同步是科学界广泛关注的课题，其应用范围涵盖从神经到社会和动物网络以及技术系统。这些网络大多数是有向的，信息或能量的流动从给定的节点单向传播到其他节点。然而，大多数关于簇同步的工作都集中在无向网络上。在这里，我们描述了一般有向网络中的簇同步。我们的第一个观察结果是，在有向网络中，节点簇 A 可能单向依赖于另一个节点簇 B：在这种情况下，只要 B 稳定，A 就可以保持同步，但反之则不然。本文的主要贡献是一种将簇稳定性问题转化为不可约形式的方法。通过这种方式，我们将原始问题分解为最低维度的子问题，从而可以立即检测到簇之间的相互依赖关系。我们将我们的分析应用于两个感兴趣的例子，一个是人类小提琴演奏者执行乐曲的网络，其中有向相互作用可以由音乐家激活或去激活，另一个是具有有向层到层连接的多层神经网络。
