Anticipated Synchronization: Numerical and Theoretical Study

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.