Nazerian Amirhossein, Panahi Shirin, Leifer Ian, Phillips David, Makse Hernán A, Sorrentino Francesco
Department of Mechanical Engineering, University of New Mexico, Albuquerque, New Mexico 87131, USA.
Levich Institute and Physics Department, City College of New York, New York, New York 10031, USA.
Chaos. 2022 Apr;32(4):041101. doi: 10.1063/5.0076412.
The main motivation for this paper is to characterize network synchronizability for the case of cluster synchronization (CS), in an analogous fashion to Barahona and Pecora [Phys. Rev. Lett. 89, 054101 (2002)] for the case of complete synchronization. We find this problem to be substantially more complex than the original one. We distinguish between the two cases of networks with intertwined clusters and no intertwined clusters and between the two cases that the master stability function is negative either in a bounded range or in an unbounded range of its argument. Our proposed definition of cluster synchronizability is based on the synchronizability of each individual cluster within a network. We then attempt to generalize this definition to the entire network. For CS, the synchronous solution for each cluster may be stable, independent of the stability of the other clusters, which results in possibly different ranges in which each cluster synchronizes (isolated CS). For each pair of clusters, we distinguish between three different cases: Matryoshka cluster synchronization (when the range of the stability of the synchronous solution for one cluster is included in that of the other cluster), partially disjoint cluster synchronization (when the ranges of stability of the synchronous solutions partially overlap), and complete disjoint cluster synchronization (when the ranges of stability of the synchronous solutions do not overlap).
本文的主要动机是以类似于巴拉霍纳和佩科拉 [《物理评论快报》89, 054101 (2002)] 研究完全同步情况的方式，来刻画簇同步（CS）情况下的网络同步性。我们发现这个问题比原来的问题要复杂得多。我们区分了具有交织簇的网络和没有交织簇的网络这两种情况，以及主稳定性函数在其自变量的有界范围或无界范围内为负的两种情况。我们提出的簇同步性定义基于网络中每个单独簇的同步性。然后我们尝试将这个定义推广到整个网络。对于CS，每个簇的同步解可能是稳定的，与其他簇的稳定性无关，这导致每个簇同步的范围可能不同（孤立CS）。对于每对簇，我们区分三种不同情况：套娃簇同步（当一个簇的同步解的稳定范围包含在另一个簇的稳定范围内时）、部分不相交簇同步（当同步解的稳定范围部分重叠时）和完全不相交簇同步（当同步解的稳定范围不重叠时）。
