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Coupled cell networks: minimality
Author(s) -
Aguiar Manuela A. D.,
Dias Ana Paula S.
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700991
Subject(s) - ode , class (philosophy) , adjacency list , homogeneous , mathematics , equivalence (formal languages) , graph , adjacency matrix , characterization (materials science) , discrete mathematics , computer science , combinatorics , physics , artificial intelligence , optics
Non‐isomorphic coupled cell networks with the same number of cells and with equivalent dynamics are said to be ODE‐equivalent. Moreover, they are all related by a linear algebra condition involving their graph adjacency matrices. A network in an ODE‐class is said to be minimal if it has a minimum number of edges among all the networks of the class. In this short paper we review the characterization of the minimal networks of an ODE‐equivalence class and we present an example for the case of non‐homogeneous networks. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)