Multi-scaled turbulence in large populations of oscillators in a diffusive medium

Large populations of oscillatory units distributed densely and uniformly in a diffusive medium exhibit turbulence with multi-scaling properties similar to fully developed fluid turbulence. Unlike the latter, however, the scaling exponents are parameter-dependent, and there exists a critical condition for the onset of individual motion of the oscillators. A three-component reaction-diffusion model is numerically analyzed to demonstrate our assertion. The universality of this type of turbulence which extends far beyond the reaction-diffusion systems is also discussed.