  We study a network of finitely many interacting clusters where each cluster
is a collection of globally coupled circle maps in the thermodynamic (or mean
field) limit. The state of each cluster is described by a probability measure,
and its evolution is given by a self-consistent transfer operator. A cluster is
synchronized if its state is a Dirac measure. We provide sufficient conditions
for all clusters to synchronize and we describe setups where the conditions are
met thanks to the uncoupled dynamics and/or the (diffusive) nature of the
coupling. We also give sufficient conditions for partially synchronized states
to arise -- i.e. states where only a subset of the clusters is synchronized --
due to the forcing of a group of cluster on the rest of the network. Lastly, we
use this framework to show emergence and stability of chimera states for these
systems.
