Coupled map systems are simple models of a finite or infinite network
of interacting units. The dynamics of the compound system is given by
the composition of the (typically chaotic) individual dynamics and a
coupling map representing the characteristics of the interaction. The
coupling map usually includes a parameter s in [0,1], representing the
strength of interaction. The main interest in such models lies in the
emergence of bifurcations when s is varied. We first introduce our
results for small finite systems. Then we initiate a new point of view
which focuses on the evolution of distributions and allows to
incorporate the investigation of a continuum of sites.