Delayed coupling of logistic maps
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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 n1, and the slave is a delayed logistic map with a delay n2. We show that when the slave system has no delay (n2=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+n1)=x(i)]. When n2¿0, a regime of generalized synchronization is observed, where y(i+n1) 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.
CitationMasoller, C.; Cavalcante, H.; Rios Leite, J. Delayed coupling of logistic maps. "Physical review E: statistical, nonlinear, and soft matter physics", Agost 2001, vol. 64, núm. 3, p. 037202-1-037202-4.