ABSTRACT
This chapter begins with a discussion of what it mean by a coupled cell system. It shows how some of the examples of static equivariant bifurcations and heteroclinic cycles provides useful phenomenological models for symmetrically coupled systems of identical cells. The chapter describes some simple examples of cycling chaos. It shows the frameworks on which to develop insights into systems of coupled cells, where one should emphasize that most of results hold for approximately symmetric systems of approximately identical cells. The chapter also describes the presence of invariant subspaces, rather than symmetry per se, that yields most, if not all, of the complex dynamical behavior. A natural way of constructing coupled cell systems is to assume internal symmetries and impose symmetry constraints on the coupling functions.
