Scaling Behavior of Turbulent Oscillators with Non-Local Interaction

Abstract

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-devleoped Navier-Stokes turbulence except that our exponents change continuously with the coupling strength.