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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
##### Keywords:
critical coupling strength; master-slave coupling