Various Synchronization Phenomena in Discrete-Time Coupled Chaotic Rotors

Abstract

Various synchronizations and related phenomena in discrete-time coupled chaotic rotors are studied. For unidirectional and bidirectional couplings, various dynamical forms of chaotic phase synchronization (CPS) and their relation to the Lyapunov spectra are shown. For a small positive maximum Lyapunov exponent of the coupled element in the case of the unidirectional coupling, the coupling strength at which CPS is achieved almost coincides with the coupling strength at which generalized synchronization (GS) is achieved. On the other hand, for a large positive maximum Lyapunov exponent, the coupling strength is much smaller on the CPS transition point than on the GS transition point. Statistical properties of the phase difference are analytically and numerically studied by large-deviation analysis. On the basis of the grand canonical formalism, the fluctuation spectrum is theoretically derived, which is compared with the numerical results. These agree with the theoretical estimation, and large deviations are detected out of the domain in which the central limit theorem cannot be applied.