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 d<3 the correlations decay exponentially at large distances or long times. For d≥3 the correlations exhibit a power law decay as the inverse of the distance or time.
Solvable model of spatiotemporal chaos
Authors: D. Hansel and H. Sompolinsky
Year of publication: 1993
Journal: Phys. Rev. Lett. 71, 2710 – Published 25 October 1993
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