On multistability near the boundary of generalized synchronization in unidirectionally coupled chaotic systems.

Multistability in the intermittent generalized synchronization regime in unidirectionally coupled chaotic systems has been found. To study such a phenomenon, the method for revealing the existence of multistable states in interacting systems being the modification of an auxiliary system approach has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled logistic maps and Rössler systems being in the intermittent generalized synchronization regime. The quantitative characteristic of multistability has been introduced into consideration.

Intermittent route to generalized synchronization in bidirectionally coupled chaotic oscillators.

The type of transition from asynchronous behavior to the generalized synchronization regime in mutually coupled chaotic oscillators has been studied. To separate the epochs of the synchronous and asynchronous motion in time series of mutually coupled chaotic oscillators, a method based on the local Lyapunov exponent calculation has been proposed. The efficiency of the method has been testified using the examples of unidirectionally coupled dynamical systems for which the type of transition is well known. The transition to generalized synchronization regime in mutually coupled systems has been shown to be an on-off intermittency as well as in the case of the unidirectional coupling.

Artificial neural network detects human uncertainty.

Artificial neural networks (ANNs) are known to be a powerful tool for data analysis. They are used in social science, robotics, and neurophysiology for solving tasks of classification, forecasting, pattern recognition, etc. In neuroscience, ANNs allow the recognition of specific forms of brain activity from multichannel EEG or MEG data. This makes the ANN an efficient computational core for brain-machine systems. However, despite significant achievements of artificial intelligence in recognition and classification of well-reproducible patterns of neural activity, the use of ANNs for recognition and classification of patterns in neural networks still requires additional attention, especially in ambiguous situations. According to this, in this research, we demonstrate the efficiency of application of the ANN for classification of human MEG trials corresponding to the perception of bistable visual stimuli with different degrees of ambiguity. We show that along with classification of brain states associated with multistable image interpretations, in the case of significant ambiguity, the ANN can detect an uncertain state when the observer doubts about the image interpretation. With the obtained results, we describe the possible application of ANNs for detection of bistable brain activity associated with difficulties in the decision-making process.

Amplification through chaotic synchronization in spatially extended beam-plasma systems.

In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.

Intermittency of intermittencies.

A phenomenon of intermittency of intermittencies is discovered in the temporal behavior of two coupled complex systems. We observe for the first time the coexistence of two types of intermittent behavior taking place simultaneously near the boundary of the synchronization regime of coupled chaotic oscillators. This phenomenon is found both in the numerical and physiological experiments. The laws for both the distribution and mean length of laminar phases versus the control parameter values are analytically deduced. A very good agreement between the theoretical results and simulation is shown.

Jump intermittency as a second type of transition to and from generalized synchronization.

The transition from asynchronous dynamics to generalized chaotic synchronization and then to completely synchronous dynamics is known to be accompanied by on-off intermittency. We show that there is another (second) type of the transition called jump intermittency which occurs near the boundary of generalized synchronization in chaotic systems with complex two-sheeted attractors. Although this transient behavior also exhibits intermittent dynamics, it differs sufficiently from on-off intermittency supposed hitherto to be the only type of motion corresponding to the transition to generalized synchronization. This type of transition has been revealed and the underling mechanism has been explained in both unidirectionally and mutually coupled chaotic Lorenz and Chen oscillators. To detect the epochs of synchronous and asynchronous motion in mutually coupled oscillators with complex topology of an attractor a technique based on finding time intervals when the phase trajectories are located on equal or different sheets of chaotic attractors of coupled oscillators has been developed. We have also shown that in the unidirectionally coupled systems the proposed technique gives the same results that may obtained with the help of the traditional method using the auxiliary system approach.

Zero Lyapunov exponent in the vicinity of the saddle-node bifurcation point in the presence of noise.

We consider a behavior of the zero Lyapunov exponent in the vicinity of the bifurcation point that occurs as the result of the interplay between dynamical mechanisms and random dynamics. We analytically deduce the laws for the dependence of this Lyapunov exponent on the control parameter both above and below the bifurcation point. The developed theory is applicable both to the systems with the random force and to the deterministic chaotic oscillators. We find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations. We also discuss how the revealed regularities are expected to take place in other relevant physical circumstances.

Incomplete noise-induced synchronization of spatially extended systems.

A type of noise-induced synchronous behavior is described. This phenomenon, called incomplete noise-induced synchronization, arises for one-dimensional Ginzburg-Landau equations driven by common noise. The mechanisms resulting in incomplete noise-induced synchronization in spatially extended systems are revealed analytically. Different types of model noise are considered. A very good agreement between the theoretical results and the numerically calculated data is shown.

Synchronization in networks of spatially extended systems.

Synchronization processes in networks of spatially extended dynamical systems are analytically and numerically studied. We focus on the relevant case of networks whose elements (or nodes) are spatially extended dynamical systems, with the nodes being connected with each other by scalar signals. The stability of the synchronous spatio-temporal state for a generic network is analytically assessed by means of an extension of the master stability function approach. We find an excellent agreement between the theoretical predictions and the data obtained by means of numerical calculations. The efficiency and reliability of this method is illustrated numerically with networks of beam-plasma chaotic systems (Pierce diodes). We discuss also how the revealed regularities are expected to take place in other relevant physical and biological circumstances.

Multiscale neural connectivity during human sensory processing in the brain.

Stimulus-related brain activity is considered using wavelet-based analysis of neural interactions between occipital and parietal brain areas in alpha (8-12 Hz) and beta (15-30 Hz) frequency bands. We show that human sensory processing related to the visual stimuli perception induces brain response resulted in different ways of parieto-occipital interactions in these bands. In the alpha frequency band the parieto-occipital neuronal network is characterized by homogeneous increase of the interaction between all interconnected areas both within occipital and parietal lobes and between them. In the beta frequency band the occipital lobe starts to play a leading role in the dynamics of the occipital-parietal network: The perception of visual stimuli excites the visual center in the occipital area and then, due to the increase of parieto-occipital interactions, such excitation is transferred to the parietal area, where the attentional center takes place. In the case when stimuli are characterized by a high degree of ambiguity, we find greater increase of the interaction between interconnected areas in the parietal lobe due to the increase of human attention. Based on revealed mechanisms, we describe the complex response of the parieto-occipital brain neuronal network during the perception and primary processing of the visual stimuli. The results can serve as an essential complement to the existing theory of neural aspects of visual stimuli processing.

Two types of phase synchronization destruction.

In this paper we report that there are two different types of destruction of the phase synchronization (PS) regime of chaotic oscillators depending on the parameter mismatch as well as in the case of the classical synchronization of periodic oscillators. When the parameter mismatch of the interacting chaotic oscillators is small enough, the PS breaking takes place without the destruction of the phase coherence of chaotic attractors of oscillators. Alternatively, due to the large frequency detuning, the PS breaking is accomplished by loss of the phase coherence of the chaotic attractors.

Detection of synchronization from univariate data using wavelet transform.

A method is proposed for detecting from univariate data the presence of synchronization of a self-sustained oscillator by external driving with varying frequency. The method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other. We apply our method to a driven asymmetric van der Pol oscillator, experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series. In the latest case, the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure.

Length distribution of laminar phases for type-I intermittency in the presence of noise.

We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-I intermittency and random dynamics. We analytically deduce the laws for the distribution of the laminar phases, with the law for the mean length of the laminar phases versus the critical parameter deduced earlier [W.-H. Kye and C.-M. Kim, Phys. Rev. E 62, 6304 (2000)] being the corollary fact of the developed theory. We find a very good agreement between the theoretical predictions and the data obtained by means of both the experimental study and numerical calculations. We discuss also how this mechanism is expected to take place in other relevant physical circumstances.

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 network's 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.

Absence Seizure Control by a Brain Computer Interface.

The ultimate goal of epileptology is the complete abolishment of epileptic seizures. This might be achieved by a system that predicts seizure onset combined with a system that interferes with the process that leads to the onset of a seizure. Seizure prediction remains, as of yet, unresolved in absence-epilepsy, due to the sudden onset of seizures. We have developed a real-time absence seizure prediction algorithm, evaluated it and implemented it in an on-line, closed-loop brain stimulation system designed to prevent the spike-wave-discharges (SWDs), typical for absence epilepsy, in a genetic rat model. The algorithm corretly predicted 88% of the SWDs while the remaining were quickly detected. A high number of false-positive detections occurred mainly during light slow-wave-sleep. Inclusion of criteria to prevent false-positives greatly reduced the false alarm rate but decreased the sensitivity of the algoritm. Implementation of the latter version into a closed-loop brain-stimulation-system resulted in a 72% decrease in seizure activity. In contrast to long standing beliefs that SWDs are unpredictable, these results demonstrate that they can be predicted and that the development of closed-loop seizure prediction and prevention systems is a feasable step towards interventions to attain control and freedom from epileptic seizures.

Macroscopic and microscopic spectral properties of brain networks during local and global synchronization.

We introduce a practical and computationally not demanding technique for inferring interactions at various microscopic levels between the units of a network from the measurements and the processing of macroscopic signals. Starting from a network model of Kuramoto phase oscillators, which evolve adaptively according to homophilic and homeostatic adaptive principles, we give evidence that the increase of synchronization within groups of nodes (and the corresponding formation of synchronous clusters) causes also the defragmentation of the wavelet energy spectrum of the macroscopic signal. Our methodology is then applied to getting a glance into the microscopic interactions occurring in a neurophysiological system, namely, in the thalamocortical neural network of an epileptic brain of a rat, where the group electrical activity is registered by means of multichannel EEG. We demonstrate that it is possible to infer the degree of interaction between the interconnected regions of the brain during different types of brain activities and to estimate the regions' participation in the generation of the different levels of consciousness.

Classifying the Perceptual Interpretations of a Bistable Image Using EEG and Artificial Neural Networks.

In order to classify different human brain states related to visual perception of ambiguous images, we use an artificial neural network (ANN) to analyze multichannel EEG. The classifier built on the basis of a multilayer perceptron achieves up to 95% accuracy in classifying EEG patterns corresponding to two different interpretations of the Necker cube. The important feature of our classifier is that trained on one subject it can be used for the classification of EEG traces of other subjects. This result suggests the existence of common features in the EEG structure associated with distinct interpretations of bistable objects. We firmly believe that the significance of our results is not limited to visual perception of the Necker cube images; the proposed experimental approach and developed computational technique based on ANN can also be applied to study and classify different brain states using neurophysiological data recordings. This may give new directions for future research in the field of cognitive and pathological brain activity, and for the development of brain-computer interfaces.

Detecting synchronization of self-sustained oscillators by external driving with varying frequency.

We propose a method for detecting the presence of a synchronization of a self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of the self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to a driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.

Coexistence of intermittencies in the neuronal network of the epileptic brain.

Intermittent behavior occurs widely in nature. At present, several types of intermittencies are known and well-studied. However, consideration of intermittency has usually been limited to the analysis of cases when only one certain type of intermittency takes place. In this paper, we report on the temporal behavior of the complex neuronal network in the epileptic brain, when two types of intermittent behavior coexist and alternate with each other. We prove the presence of this phenomenon in physiological experiments with WAG/Rij rats being the model living system of absence epilepsy. In our paper, the deduced theoretical law for distributions of the lengths of laminar phases prescribing the power law with a degree of -2 agrees well with the experimental neurophysiological data.

Separation of coexisting dynamical regimes in multistate intermittency based on wavelet spectrum energies in an erbium-doped fiber laser.

We propose a method for the detection and localization of different types of coexisting oscillatory regimes that alternate with each other leading to multistate intermittency. Our approach is based on consideration of wavelet spectrum energies. The proposed technique is tested in an erbium-doped fiber laser with four coexisting periodic orbits, where external noise induces intermittent switches between the coexisting states. Statistical characteristics of multistate intermittency, such as the mean duration of the phases for every oscillation type, are examined with the help of the developed method. We demonstrate strong advantages of the proposed technique over previously used amplitude methods.