Linear equivalence and ODE-equivalence for coupled cell networks

• Type: Article in International Scientific Journal
• Date: 2005

Authors

dias, aps (Author) FCUP; stewart, i (Author) Other

Journal

Title: Nonlinearity

Vol. 18 No. 2

Pages: 1003-1020

ISSN: 0951-7715

Publisher: Institute of Physics Publishing

Indexing

ISI Web of Knowledge - 22 Citations

Scopus - 23 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-000-3PR

DOI: 10.1088/0951-7715/18/3/004

Abstract (EN): Coupled cell systems are systems of ordinary differential equations or ODEs, defined by 'admissible' vector fields, associated with a network whose nodes represent variables and whose edges specify couplings between nodes. It is known that non-isomorphic networks can correspond to the same space of admissible vector fields. Such networks are said to be 'ODE-equivalent'. We prove that two networks are ODE-equivalent if and only if they determine the same space of linear vector fields; moreover, the variable associated with each node may be assumed one-dimensional for that purpose. We briefly discuss the combinatorics of the resulting linear algebra problem.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 18