Synchronization of non-chaotic dynamical systems

A synchronization mechanism driven by annealed noise is studied for two replicas of a coupled-map lattice which exhibits stable chaos (SC), i.e. irregular behavior despite a negative Lyapunov spectrum. We show that the observed synchronization transition, on changing the strength of the stochastic coupling between replicas, belongs to the directed percolation universality class. This result is consistent with the behavior of chaotic deterministic cellular automata (DCA), supporting the equivalence Ansatz between SC models and DCA. The coupling threshold above which the two system replicas synchronize is strictly related to the propagation velocity of perturbations in the system.