Applied Mathematics Seminar
Thursday (04/03/2003) at 4:00pm in 304 Pickard Hall
Department of Mathematics, University of Houston
"Coupled Cell Systems
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?
A Potpourri of Theory and Examples"
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.