This will be a follow-up of last week's talk by Dr. Mike Field. Last week, we tried to set up the basic terminology, definitions of dynamical equivalence, statement of the main results and give some examples.

The aim of this week's talk will be to present the main results and idea of the proofs. The proofs are algorithmic in nature and give a systematic way to construct the desired equivalence. These results give a complete treatment for the case of continuous coupled dynamical systems. As already mentioned, some of the results we present are unexpected and may have applications in numerical analysis and the design of systems that are robust to failures of individual units.