Synchrony and Elementary Operations on Coupled Cell Networks

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Manuela Aguiar (Author) FEP; Dias, APS (Author) FCUP; Ruan, H (Author) Other

Journal

Title: SIAM Journal on Applied Dynamical Systems

Vol. 15

Pages: 322-337

ISSN: 1536-0040

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00K-DG1

DOI: 10.1137/140980119

Abstract (EN): Given a finite graph (network), let every node (cell) represent an individual dynamics given by a system of ordinary differential equations, and every arrow (edge) encode the dynamical influence of the tail node on the head node. We have then defined a coupled cell system that is associated with the given network structure. Subspaces that are defined by equalities of cell coordinates and left invariant under every coupled cell system respecting the network structure are called synchrony subspaces. They are completely determined by the network structure and form a complete lattice under set inclusions. We analyze the transition of the lattice of synchrony subspaces of a network that is caused by structural changes in the network topology, such as deletion and addition of cells or edges, and rewirings of edges. We give sufficient, and in some cases both sufficient and necessary, conditions under which lattice elements persist or disappear.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16