Periodicity Manifestations in the Non-Locally Coupled Maps

We study how periodicity manifestations recently found in the turbulent globall coupled maps depend on the global feature of the couplings. We examine three non-locally coupled map models. In the first two, the all-to-all interaction is maintained but the coupling decreases with distance in a power and an exponential law. In the third, the interaction is uniform but cut off sharply. We find that, in all three and in dimension $D=1,2,3$, periodicity manifests universally from turbulence when the same suppression of the local mean field fluctuation is achieved by the non-local averaging.