SPORADICITY AND SYNCHRONIZATION IN ONE-DIMENSIONAL ASYMMETRICALLY COUPLED MAPS

A one-dimensional chain of sporadic maps with asymmetric nearest-neigh bour couplings is studied numerically. It is shown that in the region of strong asymmetry the system becomes spatially fully synchronized, e ven in the thermodynamic limit, while the Lyapunov exponent is zero. F or weak asymmetry the synchronization is no more complete, and the Lya punov exponent becomes positive. At variance with the case of non-spor adic maps, where the coherence length does not change in time, here th e coherence length exhibits strong fluctuations. In addition one has a clear relation between temporal and spatial chaos, i.e. a positive ef fective Lyapunov exponent corresponds to a lack of synchronization and vice versa.