Periodicity manifestations in the non-locally coupled maps

We study how periodicity manifestations recently found in the turbulent globally 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=1–3, periodicity manifests universally from turbulence when the same suppression of the local mean field fluctuation is achieved by the non-local averaging.