Y. Kuramoto et H. Nakao, ORIGIN OF POWER-LAW SPATIAL CORRELATIONS IN DISTRIBUTED OSCILLATORS AND MAPS WITH NONLOCAL COUPLING, Physical review letters, 76(23), 1996, pp. 4352-4355
It is argued that power-law spatial correlation at short distances is
a generic property of spatiotemporal chaos exhibited by active dynamic
al 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.