Enumerating ODE Equivalent Homogeneous Networks
Dynamical Systems
2011-05-25 v1 Discrete Mathematics
Abstract
We give an simple criterion for ODE equivalence in identical edge homogeneous coupled cell networks. This allows us to give a simple proof of Theorem 10.3 of Aquiar and Dias "Minimal Coupled Cell Networks", which characterizes minimal identical edge homogeneous coupled cell networks. Using our criterion we give a formula for counting homogeneous coupled cell networks up to ODE equivalence. Our criterion is purely graph theoretic and makes no explicit use of linear algebra.
Cite
@article{arxiv.1105.4812,
title = {Enumerating ODE Equivalent Homogeneous Networks},
author = {Alistair J. Windsor},
journal= {arXiv preprint arXiv:1105.4812},
year = {2011}
}
Comments
11 pages, 4 figures, 3 tables