SCALING BEHAVIOR OF TURBULENT OSCILLATORS WITH NONLOCAL INTERACTION

A general class of models is proposed for populations of biologically oscillating cells secreting substance whose rapid diffusion mediates the cell-cell interaction. Under certain conditions, such models are reduced to a system of non-locally coupled oscillators of the Ginzburg Landau type. The last model in space dimension one is analyzed numerically, and some remarkable features of the turbulence generated are revealed. In particular, the correlations and fluctuations obey a power law similar to the one in the fully-developed Navier-Stokes turbulence except that our exponents change continuously with the coupling strength.