Maria K. Kurovskaya

Relationship between phase synchronization of chaotic oscillators and time scale synchronization

The relationship between the phase synchronization of chaotic oscillators and their time scale synchronization has been considered, and it is established that the onset of the time scale synchronization depends on the resolving power of the base wavelet. This synchronization usually appears either before or (if said resolving power is insufficient) simultaneously with the onset of phase synchronization. The results are illustrated in the case of one-way coupled Rössler type dynamical systems.

Two Scenarios of Breaking Chaotic Phase Synchronization

Two types of phase synchronization (accordingly, two scenarios of breaking phase synchronization) between coupled stochastic oscillators are shown to exist depending on the discrepancy between the control parameters of interacting oscillators, as in the case of classical synchronization of periodic oscillators. If interacting stochastic oscillators are weakly detuned, the phase coherency of the attractors persists when phase synchronization breaks. Conversely, if the control parameters differ considerably, the chaotic attractor becomes phase-incoherent under the conditions of phase synchronization break.

Distribution of laminar phases at eyelet-type intermittency

The distribution of laminar phases in a system of two coupled chaotic oscillators has been studied in the regime of eyelet-type intermittency observed near the boundary of phase synchronization. It is established for the first time that the distribution of laminar phases in this case obeys an exponential law.

Influence of noise on the behavior of oscillators near the synchronization boundary

Nonautonomous behavior of oscillators in the presence of noise is considered. The influence of noise on the dynamics of local zero Lyapunov exponents for nonautonomous dynamic systems that are near the synchronization boundary is considered. It is shown that the action of noise on a nonautonomous dynamic system that is near the synchronization boundary produces domains of synchronous motion in the series realization, which alternate with asynchronous domains. In accordance with this, the distribution of local zero Lyapunov exponents corresponding to laminar phases shift toward negative values. This effect is demonstrated with a discrete-time system (map of a circle onto itself) that is a reference model to describe the synchronization phenomenon and also with a reference system exhibiting chaotic dynamics (Ressler system).

Self-similarity in explosive synchronization of complex networks

We report that explosive synchronization of networked oscillators (a process through which the transition to coherence occurs without intermediate stages but is rather characterized by a sudden and abrupt jump from the networks asynchronous to synchronous motion) is related to self-similarity of synchronous clusters of different size. Self-similarity is revealed by destructing the network synchronous state during the backward transition and observed with the decrease of the coupling strength between the nodes of the network. As illustrative examples, networks of Kuramoto oscillators with different topologies of links have been considered. For each one of such topologies, the destruction of the synchronous state goes step by step with self-similar configurations of interacting oscillators. At the critical point, the invariance of the phase distribution in the synchronized cluster with respect to the cluster size is reported.

Method for separating laminar and turbulent intervals in intermittent time series of systems near the phase synchronization boundary

A new method is proposed for separating the intervals of synchronous (laminar) and asynchronous (turbulent) behavior in intermittent time series of coupled chaotic systems occurring near the boundary of the phase synchronization regime. Using this method, it is possible to determine the durations of turbulent and laminar intervals, which are necessary for an analysis of the statistical characteristics of a given dynamical system. The proposed approach directly employs the instantaneous phases of chaotic signals and provides exact values of the durations of turbulent and laminar intervals in the system behavior. The validity of the new method is verified by a comparison of the results to analogous data obtained previously, which shows their good agreement.

Self-similarity of the desynchronization process in a network of generalized Kuramoto oscillators

The phenomenon of explosive synchronization in a network of generalized Kuramoto oscillators is considered. It has been shown that this process results from self-similarity observed after the loss of stability by synchronous clusters of different dimensions. The appearance of self-similarity can be revealed when studying the processes of destruction in the synchronous state of a network. It has been demonstrated that a system passes through a sequence of self-similar configurations of interacting oscillators after the abrupt destruction of a synchronous regime.

Intermittency in electric brain activity in the perception of ambiguous images

Present paper is devoted to the study of intermittency during the perception of bistable Necker cube image being a good example of an ambiguous object, with simultaneous measurement of EEG. Distributions of time interval lengths corresponding to the left-oriented and right-oriented cube perception have been obtain. EEG data have been analyzed using continuous wavelet transform and it was shown that the destruction of alpha rhythm with accompanying generation of high frequency oscillations can serve as a marker of Necker cube recognition process.

Intermittent behavior in the brain neuronal network in the perception of ambiguous images

Characteristics of intermittency during the perception of ambiguous images have been studied in the case the Necker cube image has been used as a bistable object for demonstration in the experiments, with EEG being simultaneously measured. Distributions of time interval lengths corresponding to the left-oriented and right-oriented Necker cube perception have been obtain. EEG data have been analyzed using continuous wavelet transform which was shown that the destruction of alpha rhythm with accompanying generation of high frequency oscillations can serve as a electroencephalographical marker of Necker cube recognition process in human brain.

Demonstration of brain noise on human EEG signals in perception of bistable images

In this report we studied human brain activity in the case of bistable visual perception. We proposed a new approach for quantitative characterization of this activity based on analysis of EEG oscillatory patterns and evoked potentials. Accordingly to theoretical background, obtained experimental EEG data and results of its analysis we studied a characteristics of brain activity during decision-making. Also we have shown that decisionmaking process has the special patterns on the EEG data.