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Anticipated synchronization in coupled chaotic maps with delays. (English) Zbl 0973.37033

Summary: We study the synchronization of two chaotic maps with unidirectional (master-slave) coupling. Both maps have an intrinsic delay \(n_1\), 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 analytically, and we find that they are independent of the coupling delay \(n_2\). These results 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.

MSC:

37H99 Random dynamical systems
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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