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We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase difference, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that
We study the dynamics of Lyapunov vectors in various models of one-dimensional distributed systems with spacetime chaos. We demonstrate that the vector corresponding to the maximum exponent is always localized and the localization region wanders irregularly. This localization is explained by interpreting the logarithm of the Lyapunov vector as a roughening interface. We show that for many systems, the `interface' belongs to the Kardar-Parisi- Zhang universality class. Accordingly, we discuss the scaling behaviour of finite-size effects and self-averaging properties of the Lyapunov exponents.
The quasiperiodically forced logistic map is analyzed at the terminal point of the torus-doubling bifurcation curve, where the dynamical regimes of torus, doubled torus, strange nonchaotic attractor, and chaos meet. Using the renormalization group approach we reveal scaling properties both for the critical attractor and for the parameter plane topography near the critical point.
We study spatially localized excitations in a lattice of coupled standard maps. Time-periodic solutions (breathers) exist in a range of coupling that is shown to shrink as the period grows to infinity, thus excluding the possibility of time-quasiperiodic breathers. The evolution of initially localized chaotic and quasiperiodic states in a lattice is studied numerically. Chaos is demonstrated to spread