Regular synchrony lattices for product coupled cell networks

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Manuela Aguiar (Author) FEP; Ana Dias (Author) FCUP

Journal

Title: Chaos

Vol. 25 No. 1

Final page: 013108

ISSN: 1054-1500

Publisher: American Institute of Physics

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 6 Citations

Scientific classification

CORDIS: Physical sciences > Mathematics

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-00A-6YS

DOI: 10.1063/1.4905703

Abstract (EN): There are several ways for constructing (bigger) networks from smaller networks. We consider here the cartesian and the Kronecker (tensor) product networks. Our main aim is to determine a relation between the lattices of synchrony subspaces for a product network and the component networks of the product. In this sense, we show how to obtain the lattice of regular synchrony subspaces for a product network from the lattices of synchrony subspaces for the component networks. Specifically, we prove that a tensor of subspaces is of synchrony for the product network if and only if the subspaces involved in the tensor are synchrony subspaces for the component networks of the product. We also show that, in general, there are (irregular) synchrony subspaces for the product network that are not described by the synchrony subspaces for the component networks, concluding that, in general, it is not possible to obtain the all synchrony lattice for the product network from the corresponding lattices for the component networks. We also make the following remark concerning the fact that the cartesian and Kronecker products, as graph operations, are quite different, implying that the associated coupled cell systems have distinct structures. Although, the kinds of dynamics expected to occur are difficult to compare, we establish an inclusion relation between the lattices of synchrony subspaces for the cartesian and Kronecker products. (C) 2015 AIP Publishing LLC.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 10