Sporadicity and synchronization in one-dimensional asymmetrically coupled maps

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