 
Summary: The Center for Control, Dynamical Systems, and Computation
University of California at Santa Barbara
Winter 2010 Seminar Series
Presents
Dynamics, Inflation and Equivalence of Networks of
Coupled Dynamical Systems
Mike Field
University of Houston
Wednesday, March 17, 2010, 10:00 11:00am HFH 4164
Abstract:
We describe an approach to the dynamics of coupled systems that is inspired by linear systems theory, transfer
function methodology and analog computing. The setup is broad enough to encompass continuous dynami
cal systems (ODEs) with general phase spaces, discrete dynamical systems and hybrid systems. We start by
describing the idea of dynamical equivalence of network architecture and describe a recent (algorithmic) result
that shows that if two network architectures are dynamically equivalent then any system in one architecture can
be realized by a system with the second architecture built using the cells of the first system. This turns out to be
interesting even if the architectures are the same! We illustrate the combinatorial and constructive aspects of our
approach with the example of "inflation" and give some simple examples of how robust heteroclinic cycles and
switching networks can occur in small asymmetric networks with low dimensional dynamics as well as how one
can use inflation to construct, in a controlled way, networks which admit multiple synchrony subspaces. Parts
