Enumerating ODE Equivalent Homogeneous Networks

Details Enumerating ODE Equivalent Homogeneous Networks Enumerating ODE Equivalent Homogeneous Networks

2011-05-24

arxiv.org/abs/1105.4812v1

Mathematics

Dynamical Systems

11 pages, 4 figures, 3 tables

Scientific paper

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.

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