Minimal coupled cell networks

• Type: Article in International Scientific Journal
• Date: 2007

Authors

aguiar, mad (Author) FEP; dias, aps (Author) FCUP

Journal

Title: Nonlinearity

Vol. 20 No. 1

Pages: 193-219

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 9 Citations

ISI Web of Science

Scopus - 9 Citations

Scientific classification

FOS: Natural sciences > Mathematics

CORDIS: Physical sciences > Mathematics

Other information

Authenticus ID: P-004-E1N

DOI: 10.1088/0951-7715/20/1/012

Abstract (EN): It is known that non-isomorphic coupled cell networks can have equivalent dynamics. Such networks are said to be ODE-equivalent and are related by a linear algebra condition involving their graph adjacency matrices. A network in an ODE-equivalence class is said to be minimal if it has a minimum number of edges. When studying a given network in an ODE-class it can be of great value to study instead a minimal network in that class. Here we characterize the minimal networks of an ODE-equivalence class-the canonical normal forms of the ODE-class. Moreover, we present an algorithm that computes the canonical normal forms for a given ODE-class. This goes through the calculation of vectors with minimum length contained in a cone of a lattice described in terms of the adjacency matrices of any network in the ODE-class.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 27