Enumerating periodic patterns of synchrony via finite bidirectional networks

• Type: Article in International Scientific Journal
• Date: 2010

Authors

dias, aps (Author) FCUP; pinho, em (Author) Other

Journal

Title: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Vol. 466

Pages: 891-910

ISSN: 1364-5021

Publisher: The Royal Society

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-003-8B8

DOI: 10.1098/rspa.2009.0404

Abstract (EN): Periodic patterns of synchrony are lattice networks whose cells are coloured according to a local rule, or balanced colouring, and such that the overall system has spatial periodicity. These patterns depict the finite-dimensional flow-invariant subspaces for all the lattice dynamical systems, in the given lattice network, that exhibit those periods. Previous results relate the existence of periodic patterns of synchrony, in n-dimensional Euclidean lattice networks with nearest neighbour coupling architecture, with that of finite coupled cell networks that follow the same colouring rule and have all the couplings bidirectional. This paper addresses the relation between periodic patterns of synchrony and finite bidirectional coloured networks. Given an n-dimensional Euclidean lattice network with nearest neighbour coupling architecture, and a colouring rule with k colours, we enumerate all the periodic patterns of synchrony generated by a given finite network, or graph. This enumeration is constructive and based on the automorphisms group of the graph.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20