Spatial correlations and synchronization in coupled map lattices with long-range interactions

We used numerical diagnostics to quantify spatial disorder, and its relation with temporal chaos, for a one-dimensional chain of coupled logistic maps with a coupling strength which varies with the lattice distance in a power-law fashion. The main tool is spatial return plots, whose properties are used to obtain information about the chaotic synchronized states of the system. A spatial correlation integral is introduced to characterize the clustering of points in the spatial return plots.