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Anticipated Synchronization: Numerical and Theoretical Study

Ciszak, Marzena (Directors C.R. Mirasso, R. Toral)
PhD thesis , (2006)

In this thesis we study the phenomena of synchronization between two or more constituents coupled in an unidirectional way. The coupling is designed in a way which permits the occurrence of achronal synchronization, more specifically anticipated synchronization. Anticipated synchronization refers to the situation in which one system synchronizes to the future dynamics of other system. The framework of this thesis touches many problems related to dynamical systems, for which we characterize the occurrence of anticipated synchronization with a special interest in excitable and spatiotemporal ones. We provide a theoretical description of the phenomenon, mostly through numerical simulations, but also in the particular case of excitable systems, through experimental results. Moreover we model the anticipation of the chemical reaction consisting on the oxidation of the CO on the platinum surface and provide the study from a point of view of the experimental requisites and limitations. We show that spatially separated and coupled excitable cells with the anticipated synchronization scheme under particular conditions may contribute to zero-lag synchronization. We relate this result to the experimental observation of zero-lag synchronization between spatially separated brain areas. Considering further spatiotemporal dynamics we demonstrate on the example of coupled cellular automata the equivalence between the coupling based on time-delayed and on space-delayed variables. We relate this finding to the previous study on the spatial properties of time-delayed systems. We uncover the dynamical mechanism of anticipated synchronization in excitable systems showing that the anticipation is due to the lowering of the excitability threshold of the slave by the delayed coupling term. Also we try to answer the question about the dynamical mechanism of anticipated synchronization in chaotic systems in terms of a modified system approach. Finally we estimate the practical usage of anticipated synchronization. We present a new control method which we call predict-prevent control method for excitable systems. We also compare the prediction capacity of the anticipated synchronization scheme implemented in neural networks modules with the standard prediction methods given by neural networks.