Macroscopic chaos in globally coupled maps

We study the coherent dynamics of globally coupled maps showing macroscopic chaos. With this term we indicate the hydrodynamical-like irregular behavi or of some global observables, with typical times much longer than the time s related to the evolution of the single (or microscopic) elements of the s ystem. The usual Lyapunov exponent is not able to capture the essential fea tures of this macroscopic phenomenon. Using the recently introduced notion of finite size Lyapunov exponent, we characterize, in a consistent way, the se macroscopic behaviors. Basically, at small values of the perturbation we recover the usual (microscopic) Lyapunov exponent, while at larger values a sort of macroscopic Lyapunov exponent emerges, which can be much smaller than the former. A quantitative characterization of the chaotic motion at h ydrodynamical level is then possible, even in the absence of the explicit e quations for the time evolution of the macroscopic observables, (C) 1999 El sevier Science B.V. All rights reserved.