Condensation versus independence in weakly interacting CMLs

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.