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.

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.

Feed-forward artificial neural network provides data-driven inference of functional connectivity.

We propose a new model-free method based on the feed-forward artificial neuronal network for detecting functional connectivity in coupled systems. The developed method which does not require large computational costs and which is able to work with short data trials can be used for analysis and reconstruction of connectivity in experimental multichannel data of different nature. We test this approach on the chaotic Rössler system and demonstrate good agreement with the previous well-known results. Then, we use our method to predict functional connectivity thalamo-cortical network of epileptic brain based on ECoG data set of WAG/Rij rats with genetic predisposition to absence epilepsy. We show the emergence of functional interdependence between cortical layers and thalamic nuclei after epileptic discharge onset.

Percept-related EEG classification using machine learning approach and features of functional brain connectivity.

Machine learning is a promising approach for electroencephalographic (EEG) trials classification. Its efficiency is largely determined by the feature extraction and selection techniques reducing the dimensionality of input data. Dimensionality reduction is usually implemented via the mathematical approaches (e.g., principal component analysis, linear discriminant analysis, etc.) regardless of the origin of analyzed data. We hypothesize that since EEG features are determined by certain neurophysiological processes, they should have distinctive characteristics in spatiotemporal domain. If so, it is possible to specify the set of EEG principal features based on the prior knowledge about underlying neurophysiological processes. To test this hypothesis, we consider the classification of EEG trials related to the perception of ambiguous visual stimuli. We observe that EEG features, underlying the different ambiguous stimuli interpretations, are defined by the network properties of neuronal activity. Having analyzed functional neural interactions, we specify the brain area in which neural network architecture exhibits differences for different classes of EEG trials. We optimize the feedforward multilayer perceptron and develop a strategy for the training set selection to maximize the classification accuracy, being 85% when all channels are used. The revealed localization of the percept-related features allows about 95% accuracy, when the number of channels is reduced up to 90%. Obtained results can be used for classification of EEG trials associated with more complex cognitive tasks. Taking into account that cognitive activity is subserved by a distributed functional cortical network, its topological properties have to be considered when selecting optimal features for EEG trial classification.

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.

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.

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.

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.

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.

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.

Excitation and suppression of chimera states by multiplexing.

We study excitation and suppression of chimera states in an ensemble of nonlocally coupled oscillators arranged in a framework of multiplex network. We consider the homogeneous network (all identical oscillators) with different parametric cases and interlayer heterogeneity by introducing parameter mismatch between the layers. We show the feasibility to suppress chimera states in the multiplex network via moderate interlayer interaction between a layer exhibiting chimera state and other layers which are in a coherent or incoherent state. On the contrary, for larger interlayer coupling, we observe the emergence of identical chimera states in both layers which we call an interlayer chimera state. We map the spatiotemporal behavior in a wide range of parameters, varying interlayer coupling strength and phase lag in two and three multiplexing layers. We also prove the emergence of interlayer chimera states in a multiplex network via evaluation of a continuous model. Furthermore, we consider the two-layered network of Hindmarsh-Rose neurons and reveal that in such a system multiplex interaction between layers is capable of exciting not only the synchronous interlayer chimera state but also nonidentical chimera patterns.

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.

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.

Intermittency route to chaos and broadband high-frequency generation in semiconductor superlattice coupled to external resonator.

We investigate the onset of broadband microwave chaos in the miniband semiconductor superlattice coupled to an external resonator. Our analysis shows that the transition to chaos, which is confirmed by calculation of Lyapunov exponents, is associated with the intermittency scenario. The evolution of the laminar phases and the corresponding Poincare maps with variation of a supercriticality parameter suggest that the observed dynamics can be classified as type I intermittency. We study the spatiotemporal patterns of the charge concentration and discuss how the frequency band of the chaotic current oscillations in semiconductor superlattice depends on the voltage applied.

Lyapunov exponent corresponding to enslaved phase dynamics: Estimation from time series.

A method for the estimation of the Lyapunov exponent corresponding to enslaved phase dynamics from time series has been proposed. It is valid for both nonautonomous systems demonstrating periodic dynamics in the presence of noise and coupled chaotic oscillators and allows us to estimate precisely enough the value of this Lyapunov exponent in the supercritical region of the control parameters. The main results are illustrated with the help of the examples of the noised circle map, the nonautonomous Van der Pole oscillator in the presence of noise, and coupled chaotic Rössler systems.

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.

Inapplicability of an auxiliary-system approach to chaotic oscillators with mutual-type coupling and complex networks.

The auxiliary system approach being de facto the standard for the study of generalized synchronization in the unidirectionally coupled chaotic oscillators is also widely used to examine the mutually coupled systems and networks of nonlinear elements with the complex topology of links between nodes. In this Brief Report we illustrate by two simple counterexamples that the auxiliary-system approach gives incorrect results for the mutually coupled oscillators and therefore to study the generalized synchronization this approach may be used only for the drive-response configuration of nonlinear oscillators and networks.

Generalized synchronization in mutually coupled oscillators and complex networks.

We introduce a concept of generalized synchronization, able to encompass the setting of collective synchronized behavior for mutually coupled systems and networking systems featuring complex topologies in their connections. The onset of the synchronous regime is confirmed by the dependence of the system's Lyapunov exponents on the coupling parameter. The presence of a generalized synchronization regime is verified by means of the nearest neighbor method.