Joint NSF supported research with Nikita Agarwal.

We start with a general overview of some basic problems in networks of coupled dynamical systems, computational neuro-science and engineering. We then describe some very recent work about when two networks with different topologies or architectures can be dynamically equivalent and give a complete (and algorithmic) resolution of the problem for continuous dynamics (ordinary differential equations) and partial (but almost complete) resolution for discrete dynamics. 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.

The talk is aimed for a general (graduate) audience (and RA support is possible). There will be a follow-up talk by Nikita Agarwal who will present more of the mathematical details.