Synchronization and equitable partitions in weighted networks
Synchronization and equitable partitions in weighted networks
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DOI：
10.1063/1.4997385
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发表时间：
2018-07-01
期刊：
影响因子：
2.9
通讯作者：
Dias, Ana Paula S.
中科院分区：
文献类型：
--
作者：
Aguiar, Manuela A. D.;Dias, Ana Paula S.
本文提出的工作有两个目的。一是揭示了Golubitsky、Stewart和合作者的耦合单元网络形式以一种自然的方式容纳了加权网络，也就是说，图中连接的关联权重可以是任何实数。回想一下，在前一种设置中，网络连接具有关联的非负整数值。在这里，一些中心概念和结果在前形式主义是存在的，并应用于加权设置。这些结果与同步子空间和平衡关系的存在密切相关。本文还将同步性子空间和平衡关系的概念分别与同步性集群和公平分割的概念进行了对应。这种对应意味着这两股文学的结果是联系在一起的。特别是，我们注意到，这里所述的加权耦合细胞网络的结果适用于其他文献，并给出了例子来说明这一点。AIP出版社出版。
The work presented in this paper has two purposes. One is to expose that the coupled cell network formalism of Golubitsky, Stewart, and collaborators accommodates in a natural way the weighted networks, that is, graphs where the connections have associated weights that can be any real number. Recall that, in the former setup, the network connections have associated nonnegative integer values. Here, some of the central concepts and results in the former formalism are present and applied to the weighted setup. These results are strongly associated with the existence of synchrony subspaces and balanced relations. This work also makes the correspondence between the concepts of synchrony subspace and balanced relation with those of cluster of synchrony and equitable partition, respectively, which are used in the other strand of literature. This correspondence implies that the results of these two strands of literature are linked. In particular, we remark that the results stated here for weighted coupled cell networks apply in that other strand of literature, and examples are given to illustrate that. Published by AIP Publishing.