Delayed coupling of logistic maps

Abstract

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 $\left[{y(i+n}_1\right)=x\left(i\right)\mathrm{}].$ When $n_2\ne 0,$ a regime of generalized synchronization is observed, where ${y(i+n}_1)$ is synchronized with $x\left(i\right),$ 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.