Transition to stochastic synchronization in spatially extended systems

Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dimensional systems, synchronization can be achieved only if the maximum Lyapunov exponent becomes negative for sufficiently large noise amplitude. Moreover, noise can suppress also the nonlinear mechanism of information propagation, which may be present in the spatially extended system. An example of phase transition is observed when both the linear and the nonlinear mechanisms of information production disappear at the same critical value of the noise amplitude. The corresponding critical properties cannot be estimated numerically with great accuracy, but some general argument suggests that they could be ascribed to the Kardar-Parisi-Zhang universality class. Conversely, when the nonlinear mechanism prevails on the linear one, another type of phase transition to stochastic synchronization occurs. This one is shown to belong to the universality class of directed percolation.