Origin of power-law spatial correlations in distributed oscillators and maps with nonlocal coupling

It is argued that power-law spatial correlation at short distances is a generic property of spatiotemporal chaos exhibited by active dynamical elements coupled nonlocally. While this fact was suggested earlier from some numerical analysis of coupled limit cycles, further evidence is provided here from an analysis for chaotic Rossler oscillators and logistic maps. A theory is presented to explain why such short-range nonanalyticity of correlation with parameter-dependent exponent is so universal when the coupling is nonlocal.