Predictability in spatially extended systems

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Abstract
The predictability problem is discussed in turbulent fluids and in spatially extended systems. We perform a numerical analysis of the spatial propagation of a small perturbation initially localized at a point of a one-dimensional lattice of coupled maps, where the interactions can be either local or non-local in space. In both cases, the nonlinear terms in the dynamics of the perturbation cannot be neglected and the predictability problem cannot be reduced to the linearized evolution equations. Only for non-local interactions is the predictability time proportional to the inverse Lyapunov exponent lambda , as in dynamical systems with a few degrees of freedom. For local interactions it is proportional to the size of the system and is practically independent of the chaoticity degree lambda .

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