Anticipated synchronization in coupled chaotic maps with delays

We study the synchronization of two chaotic maps with unidirectional (maste r-slave) coupling. Both maps have an intrinsic delay ni, and coupling acts with a delay n(2). Depending on the sign of the difference n(1) - n(2), the slave map can synchronize to a future or a past state of the master system . The stability properties of the synchronized state are studied analytical ly, and we find that they are independent of the coupling delay n2. These r esults are compared with numerical simulations of a delayed map that arises from discretization of the Ikeda delay-differential equation. We show that the critical value of the coupling strength above which synchronization is stable becomes independent of the delay n(1) for large delays. (C) 2001 Pu blished by Elsevier Science B.V.