Spatiotemporal chaos in one- and two-dimensional coupled map lattices

Abstract

Coupled map lattices are investigated as a model for spatiotemporal chaos. Pattern dynamics in diffusively coupled logistic lattice is briefly reviewed with the use of power spectra, domain distribution, and Lyapunov spectra. Mechanism of pattern selection with the suppression of chaos is discussed. Pattern dynamics on a 2-dimensional lattice is shown. In a weak coupling regime, a similarity with the one-dimensional case is found; frozen random pattern, selection, Brownian motion of a chaotic string, and intermittent collapse of the pattern with selective flicker noise. In a strong coupling regime, frozen pattern is found to be unstable by the surface tension, which is in contrast with the one-dimensional case. Convective coupling model is introduced in connection with the fluid turbulence of Navier-Stokes type. Soliton turbulence and vortex turbulence in the model are reported. Physical implications of coupled map lattices are discussed.