Synchronization and coherence in thermodynamic coupled map lattices with intermediate-range coupling.

In spatially extended systems, intermediate-range interactions arise naturally in some physical contexts. To study them, we investigate a model of coupled map lattices (CML's) with intermediate-range coupling, and derive analytic conditions for its synchronization. We find that in these CML's, if the range of coupling is fixed, the law of large numbers applies for the mean field. The total normalized power in nonzero components of the power spectrum of the mean field goes to zero in the thermodynamic limit. We also show that in the same limit the relevant parameter for synchronization and coherence is the fraction of sites coupled, and not their number.