Synchronization and equitable partitions in weighted networks

• Type: Article in International Scientific Journal
• Date: 2018

Authors

Manuela Aguiar (Author) FEP; dias, aps (Author) FCUP

Journal

Title: Chaos

Vol. 28

ISSN: 1054-1500

Publisher: American Institute of Physics

Indexing

ISI Web of Knowledge - 17 Citations

Scopus - 18 Citations

Other information

Authenticus ID: P-00P-DMS

DOI: 10.1063/1.4997385

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 8