Anticipated synchronization in coupled chaotic maps with delays

Details Anticipated synchronization in coupled chaotic maps with delays Anticipated synchronization in coupled chaotic maps with delays

2001-04-25

arxiv.org/abs/nlin/0104061v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 4 figures

Scientific paper

10.1016/S0378-4371(01)00362-4

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.

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