We propose a simple model unifying two major approaches to the analysis of
large multicomponent systems: interacting particle systems (IPS) and couple map
lattices (CML) and show that in the weak interaction limit depending on fine
properties of the interaction potential this model may demonstrate both
condensation/synchronization and independent motions. Note that one of the main
paradigms of the CML theory is that the latter behavior is supposed to be
generic. The model under consideration is related to dynamical networks and
sheds a new light to the problem of synchronization under weak interactions.