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?
The ideas will be illustrated through a series of examples and two main
theorems. The first theorem gives necessary and sufficient conditions
for synchrony in terms of network architecture; and the second shows that
synchronous dynamics may itself be viewed as a coupled cell system through a
quotient construction. We also show how nongeneric bifurcations with
nongeneric results arise in bifurcations in coupled systems.