Solvable model of spatiotemporal chaos

Abstract

A continuous time dynamic model of a d-dimensional lattice of coupled localized m-component chaotic elements is solved exactly in the limit m→∞. A self-consistent nonlinear partial differential equation for the correlations in space and time is derived. Near the onset of spatiotemporal disorder there are solutions that exhibit a novel space-time symmetry: the corresponding correlations are invariant to rotations in the d+1 space-time variables. For dd≥3 the correlations exhibit a power law decay as the inverse of the distance or time.