UTA Department of Mathematics

Applied Mathematics Seminar

Date/Time/Room: Thursday (04/03/2003) at 4:00pm in 304 Pickard Hall

Speaker: Martin Golubitsky, Department of Mathematics, University of Houston

"Coupled Cell Systems
A Potpourri of Theory and Examples"

Abstract: A coupled cell system is a collection of individual, but interacting, dynamical systems. Coupled cell models assume that the output from each cell is important --- not just the dynamics considered as a whole. In these systems the signals from two or more cells can be compared and patterns of activity can emerge. We ask when can the cell dynamics in a subset of cells be identical (synchrony) or differ by a phase shift. In particular: How much of the qualitative dynamics observed in coupled cells is the product of network architecture and how much is related to the specific dynamics of cells and the way they are coupled?

We illustrate the ideas through a series of examples and discuss two theorems. The first theorem classifies spatio-temporal symmetries of periodic solutions and the second gives necessary and sufficient conditions for synchrony in terms of network architecture and its symmetry groupoid. This is joint work with Ian Stewart.