Delayed coupling of logistic maps.

We study the synchronization of logistic maps in a one-way coupling configuration. The master system is coupled to the slave system with a delay n(1), and the slave is a delayed logistic map with a delay n(2). We show that when the slave system has no delay (n(2)=0), perfectly synchronized solutions exist for strong enough coupling. In these solutions the slave variable y is retarded with respect to the master variable x with a retardation equal to the delay of the coupling [y(i+n(1))=x(i)]. When n(2) not equal 0, a regime of generalized synchronization is observed, where y(i+n(1)) is synchronized with x(i), but not completely, since the master and the slave systems obey different maps. We introduced a similarity function as an indicator of the degree of synchronization and, using a noisy master source, distinguished synchronization from noise-induced correlations.