Quantitative analysis of chaotic synchronization by means of coherence

Selective properties of diffusive couplings and their influence on spatiotemporal chaos

Spatiotemporal chaos in a ring of logistic maps with symmetric diffusive couplings is investigated in dependence on the coupling strength. Spatial spectrum of oscillations is compared with the wave response of a linear spatial filter formed by couplings between maps in the ensemble. Correlation between the spectrum and the filter's amplitude-wave characteristics is considered.

Synchronization of infra-slow oscillations of brain potentials with respiration

We study the synchronization of infra-slow oscillations in human scalp electroencephalogram signal with the respiratory signal. For the cases of paced respiration with a fixed frequency and linearly increasing frequency, we reveal the phase and frequency locking of infra-slow oscillations of brain potentials by respiration. It is shown that for different brain areas, the infra-slow oscillations and respiration can exhibit synchronous regimes of different orders.

Influence of chaotic synchronization on mixing in the phase space of interacting systems

Using the concept of the relative metric entropy, we study the influence of the synchronization phenomenon on mixing rate in the phase space of deterministic and noisy chaotic systems. We show that transition to both complete and phase synchronization of chaos is accompanied by the decrease of the level of mixing induced by internal nonlinear mechanisms of interacting systems as well as by external noise influence. Therefore, the decrease of the mixing rate in the phase space of interacting systems may indicate transition to synchronization. The obtained results are important for time series analysis in various types of real noisy systems (e.g., biological, social, and financial systems).

Phase multistability and phase synchronization in an array of locally coupled period-doubling oscillators

We consider phase multistability and phase synchronization phenomena in a chain of period-doubling oscillators. The synchronization in arrays of diffusively coupled self-sustained oscillators manifests itself as rotating wave regimes, which are characterized by equal amplitudes and phases in every site which are shifted by a constant value. The value of the phase shift is preserved while the shape of motion becomes more complex through a period-doubling cascade. The number of coexisting attractors increases drastically after the transition from period-one to period-two oscillations and then after every following period-doubling bifurcation. In the chaotic region, we observe a number of phase-synchronized modes with instantaneous phases locked in different values. The loss of phase synchronization with decreasing coupling is accompanied by intermittency between several synchronous regimes.

Synchronization of stochastic oscillations due to long-range diffusion

We investigate the effect of long-range diffusive mixing on stochastic processes taking place on low-dimensional catalytic supports. As a working example, the cyclic lattice Lotka-Volterra (LLV) model is used which is conservative at the mean-field level and demonstrates fractal patterns and local oscillations when realized on low-dimensional lattice supports. We show that the local oscillations are synchronized when a weak, long-range, diffusive process is added to LLV and global oscillations of limit cycle type emerge. This phenomenon is demonstrated as a nonequilibrium phase transition and takes place when the mixing-to-reaction rate p (order parameter) is above a critical point p_{c} . The value of the critical point is shown to depend on the kinetic parameters. The global oscillations in this case emerge as a result of phase synchronization between local oscillations on sublattices.

Time shifts and correlations in synchronized chaos

We introduce a new method for predicting characteristics of the synchronized state achieved by a wide class of unidirectional coupling schemes. Specifically, we derive a transfer function from the coupling model that provides estimates of the correlation between the drive and response waveforms, and of the time shift (i.e., lag or anticipation) of the synchronized state. To demonstrate the method, we apply it to a simulated system of coupled Rossler oscillators as well as to an experimental system of coupled chaotic electronic circuits. Finally, we show that the transfer function can be exploited to design novel coupling schemes that significantly improve the correlation and increase the maximum achievable time shift.