Synchrony Breaking Bifurcations
by
Martin Golubitsky
University of Houston

A coupled cell system is a network 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: Which part of the qualitative dynamics observed in coupled cells is the product of network architecture and which part depends on the specific equations?

In our theory, local network symmetries replace symmetry as a way of organizing network dynamics, and synchrony-breaking replaces symmetry-breaking as a basic way in which transitions to complicated dynamics occur. In this talk we present some of the general theory of synchrony and some interesting examples of synchrony-breaking.

Date received: April 3, 2008