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Nearest Neighbors, Phase Tubes And Generalized Synchronization

In this paper we report for the first time on the necessity of the refinement of the concept of generalized chaotic synchronization. We show that the state vectors of the interacting chaotic systems being in the generalized synchronization regime are related with each other by the functional, but not the functional relation as it was assumed until now. We propose the phase tube approach explaining the essence of generalized synchronization and allowing the detection and the study of this regime in many relevant physical circumstances. The finding discussed in this Report gives a strong potential for new applications.