Power-law spatial correlations and the onset of individual motions in self-oscillatory media with non-local coupling

It is demonstrated numerically that power-law spatial correlations appear generically in self-oscillatory media with non-local coupling. This occurs in length scales smaller than the range of coupling when the turbulent fluctuations generated through the Benjamin-Feir instability spread deep into this regime. The associated exponent varies continuously with the coupling strength. However, the latter has a lower critical value below which the pattern can no longer sustain its spatial continuity giving way to individual motions of the oscillators. Our numerical analyses are carried out on a one-dimensional oscillator lattice where two types of model oscillators are examined. They are the complex Ginzburg-Landau type oscillators and the Brusselator. A non-trivial effect of breaking the special symmetry of the former model is also discussed.