Noise-driven Synchronization in Coupled Map Lattices

Synchronization is shown to occur in spatially extended systems under the effect of additive spatio-temporal noise. In analogy to low dimensional systems, synchronized states are observable only if the maximum Lyapunov exponent $\mathrm{\Lambda }$ is negative. However, a sufficiently high noise level can lead, in map with finite domain of definition, to nonlinear propagation of information, even in non chaotic systems. In this latter case the transition to synchronization is ruled by a new ingredient : the propagation velocity of information $V_F$. As a general statement, we can affirm that if $V_F$ is finite the time needed to achieve a synchronized trajectory grows exponentially with the system size $L$, while it increases logarithmically with $L$ when, for sufficiently large noise amplitude, $V_F=0$ .