Different regimes of synchronization in nonidentical time-delayed maps

We study the synchronization of time-delayed nonidentical maps subject to unidirectional (master–slave) coupling. The individual dynamics of the maps have a delay n1, and the coupling acts with a delay n2. We show analytically that, suitably tuning the slave map parameters, two distinct synchronization regimes can occur. In one regime, the lag time between the slave and the master maps is given by the delay of the coupling, n2, while in the other regime is given by the difference between the delays, n1−n2. We analyze the effect of the coupling strength on the different synchronization regimes in logistic and Hénon maps.