Abstract
We give a simple necessary and sufficient condition for the dynamical equivalence of
two coupled cell networks with different network architectures. The results are applicable to both continuous and discrete dynamical
systems and are framed in terms of what we term input and output equivalence.
We also give an algorithm that allows
explicit construction of the cells in a system with a given network architecture in
terms of the cells from an equivalent system with different network architecture.
Details of proofs are provided for the case of cells with asymmetric inputs --- details for
the case of symmetric inputs are provided in a companion paper.
For preprint,
email: mikefield@gmail.com
Professor Mike Field
Department of Mathematics
Imperial College
London SW7 2AZ