Bifurcations in Coupled Systems

Tuesday, March 6, 2007 - 1:30pm - 2:20pm
EE/CS 3-180
Martin Golubitsky (University of Houston)
A coupled cell system is a collection of interacting dynamical systems.
Coupled cell models assume that the output from each cell is important and
that signals from two or more cells can be compared so that patterns of
synchrony can emerge. We ask: How much of the qualitative dynamics observed
in coupled cells is the product of network architecture and how much depends
on the specific equations? Speficially we study the structure of
synchrony-breaking bifurcations in these systems.

The ideas will be illustrated through a series of examples and theorems.
One example shows how a frequency filter / amplifier can be built from a
small three-cell feed forward network; and a second illustrates patterns
of synchrony in lattice dynamical systems. One theorem gives necessary
and sufficient conditions for synchrony in terms of network architecture;
and a second shows that synchronous dynamics may itself be viewed as
dynamics in a coupled cell system through a quotient construction.

MSC Code: