The aim of the present research project is to investigate the possible synchronization transitions in extended systems and in particular to individuate the universality classes to which these out-of-equilibrium transitions belong.
Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization [40].
In analogy with low-dymensional systems, synchronization can be achieved only if the maximum Lyapunov exponent becomes negative for sufficiently large noise amplitude. Moreover, noise can suppress also the non-linear mechanism of information propagation, that may be present in the spatially extended system. A first example of phase transition is observed when both the linear and the non-linear mechanisms of information production disappear at the same critical value of the noise amplitude.
The corresponding critical properties can be hardly identified numerically, but some general argument suggests that they could be ascribed to the Kardar-Parisi-Zhang (with a hard-wall) universality class. Conversely, when the non-linear 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 (DP) [47].
Our findings have been recently confirmed by a detailed study of Ahlers & Pikovsky on two chains of coupled map lattices coupled site by site by a local coupling.
Presently we are investigating deterministic growth models (Restricted Solid on Solid Model, Single Step Model) and stochastic models with the aim to reproduce within one single model the two different out-of-equilibrium transitions observed for the synchronization of extended systems. In particular, we would like to understand the mechanisms that leads from one universality class (KPZ plus wall) to the other (DP) and the possible existence of a unifying formulation for the two scenarios. These results have been reported in the following two papers [57,59].
A new direction of research has been recently started by considering maps with power law coupling [32], in this context we have examined the origin of nonlinear synchronization in ``almost'' discontinuous maps. And we have characterized the synchronization transition for continuous and discontinuous maps [63].
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