In this paper, we investigated the fatigue-related processes of reconfiguring the human brain functional network while solving the cognitive task. We analyzed the correlations between the psychophysiological state of the subject with the characteristics of neural activity. We found that the subject’s fatigue positively correlates with the average degree of functional connectivities between neural ensembles in the beta and alpha frequency ranges. The obtained results indicate the increase in the integrative processes of a functional neural network. We revealed that the increasing fatigue during the experiment does not decrease the efficiency of the task completion: the speed and correctness of responses do not change. This suggests that functional integration may reflect the optimization of the brain’s neural network during the experiment.
We propose a new model-free method based on 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 restoration 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-know results.
In this paper, we analyze the inter-layer connectivity of multiplex functional network of the brain, where each layer represent the separate timescale. For this task we conduct the EEG experiments, which involve the solving of Schulte tables, the widespread psycological test. Using the wavelet bicoherence we reconstruct the functional network on various frequency bands of brain activity, that allows us to build multiplex functional network. Using the concept of betweenness centrality we analyze the inter-layer interaction in the brain functional network and reveal the regions, which demonstrate maximal inter-layer activity.
In this paper we propose a model of the spatially distributed network based on the spatially correlated preferential attachments. Nodes in the spatially distributed networks of the real word, such as various urban or biological networks, aren't establishing randomly: the probability of emergence of new nodes is higher in the area of already existing ones. In this work we unite two principles of the real network modeling: the correlated percolation model and preferential attachment. To regulate spatial limitations of the network, we use density gradient, which determines the decrease of the probability of the connection emergence between two nodes with increase of the distance between them. We also consider the consistency of our results in the context of the real-world system modeling.
The paper considers the phenomena of competition in multiplex network whose structure evolves corresponding to dynamics of it’s elements, forming closed loop of self-learning with the aim to reach the optimal topology. Numerical analysis of proposed model shows that it is possible to obtain scale-invariant structures for corresponding parameters as well as the structures with homogeneous distribution of connections in the layers. Revealed phenomena emerges as the consequence of the self-organization processes related to structure-dynamical selflearning based on homeostasis and homophily, as well as the result of the competition between the network’s layers for optimal topology. It was shown that in the mode of partial and cluster synchronization the network reaches scale-free topology of complex nature that is different from layer to layer. However, in the mode of global synchronization the homogeneous topologies on all layer of the network are observed. This phenomenon is tightly connected with the competitive processes that represent themselves as the natural mechanism of reaching the optimal topology of the links in variety of real-world systems.
In this paper, we study the complex multi-scale network of nonlocally coupled oscillators for the appearance of chimera states. Chimera is a special state in which, in addition to the asynchronous cluster, there are also completely synchronous parts in the system. We show that the increase of nodes in subgroups leads to the destruction of the synchronous interaction within the common ring and to the narrowing of the chimera region.
The focal riddle for physicists and neuroscientists consists in disclosing the way microscopic scale neural interactions pilot the formation of the different activities revealed (at a macroscopic scale) by EEG and MEG equipments. In the current paper we estimate the degree of the interactions between the remote regions of the brain, based on the wavelet analysis of EEG signals, recorded from these brain areas. With the help of the proposed approach we analyze the neural interactions, associated with cognitive processes, taken place in human’s brain during the perception of visual stimuli. We show that neurons in the remote regions of brain interact with the different degree of intensity in the generation of different rhythms. In particular during the perception of visual stimuli strong interaction has been observed in β - frequency band while strong interaction in α - frequency band has been observed in resting state.
The main issue of epileptology is the elimination of epileptic events. This can be achieved by a system that predicts the emergence of seizures in conjunction with a system that interferes with the process that leads to the onset of seizure. The prediction of seizures remains, for the present, unresolved in the absence epilepsy, due to the sudden onset of seizures. We developed an algorithm for predicting seizures in real time, evaluated it and implemented it into an online closed-loop brain stimulation system designed to prevent typical for the absence of epilepsy of spike waves (SWD) in the genetic rat model. The algorithm correctly predicts more than 85% of the seizures and the rest were successfully detected. Unlike the old beliefs that SWDs are unpredictable, current results show that they can be predicted and that the development of systems for predicting and preventing closed-loop capture is a feasible step on the way to intervention to achieve control and freedom from epileptic seizures.
In the report we study the mechanisms of phase synchronization in the model of adaptive network of Kuramoto phase oscillators and discuss the possibility of the further application of the obtained results for the analysis of the neural network of brain. In our theoretical study the model network represents itself as the multilayer structure, in which the links between the elements belonging to the different layers are arranged according to the competitive rule. In order to analyze the dynamical states of the multilayer network we calculate and compare the values of local and global order parameter, which describe the degree of coherence between the neighboring nodes and the elements over whole network, respectively. We find that the global synchronous dynamics takes place for the large values of the coupling strength and are characterized by the identical topology of the interacting layers and a homogeneous distribution of the link strength within each layer. We also show that the partial (or cluster) synchronization, occurs for the small values of the coupling strength, lead to the emergence of the scale-free topology, within the layers.
KEYWORDS: Oscillators, Numerical analysis, Multilayers, Analytical research, Neurons, Systems modeling, Chemical elements, Mathematical modeling, Chemical analysis, Data modeling
We numerically study the interaction between the ensembles of the Hindmarsh-Rose (HR) neuron systems, arranged in the multilayer network model. We have shown that the fully identical layers, demonstrated individually different chimera due to the initial mismatch, come to the identical chimera state with the increase of inter-layer coupling. Within the multilayer model we also consider the case, when the one layer demonstrates chimera state, while another layer exhibits coherent or incoherent dynamics. It has been shown that the interactions chimera-coherent state and chimera-incoherent state leads to the both excitation of chimera as from the ensemble of fully coherent or incoherent oscillators, and suppression of initially stable chimera state
In this paper we study the conditions of chimera states excitation in ensemble of non-locally coupled Kuramoto-Sakaguchi (KS) oscillators. In the framework of current research we analyze the dynamics of the homogeneous network containing identical oscillators. We show the chimera state formation process is sensitive to the parameters of coupling kernel and to the KS network initial state. To perform the analysis we have used the Ott-Antonsen (OA) ansatz to consider the behavior of infinitely large KS network.
In the paper we study the possibility to control the frequency of the sub-THz source, based on the semiconductor superlattice by means of optimal spatial distribution of the doping density. We propose the appropriate mathematical model, which allows to describe the collective transport of charge in miniband semiconductor, where the spatial profile of the equilibrium charge density is defined by function. As the example we consider the uniform spatial distribution of doping density, contained local inhomogeneity, caused by local increase of density and described approximately by Gaussian function. We show that such inhomogeneity being placed in different areas of the transport region can affect the dynamics of charge domain, which, in turn, leads to increase (or decrease) of the frequency of current oscillations.
In this paper we investigate the impact of competition between layers of adaptive multiplex network on pattern formation in the system under study and discuss the possibility of the further application of the obtained results for the analysis of the neural network of brain. To describe the dynamics of interacting nodes we use the Kuramoto model of coupled phase oscillators. To understand the macroscopic processes that take place in this system we calculate and compare the values of layer and global order parameter, which describe the degree of coherence between the nodes in each layer and over whole network, respectively. We find that in such adaptive network the low values of order inside layers corresponding to the formation of similar topologies among them. Nevertheless, the cluster synchronization results in divergence of layer structures from each other.
In the paper we study the mechanisms of phase synchronization in the adaptive model network of Kuramoto oscillators and the neural network of brain by consideration of the integral characteristics of the observed networks signals. As the integral characteristics of the model network we consider the summary signal produced by the oscillators. Similar to the model situation we study the ECoG signal as the integral characteristic of neural network of the brain. We show that the establishment of the phase synchronization results in the increase of the peak, corresponding to synchronized oscillators, on the wavelet energy spectrum of the integral signals. The observed correlation between the phase relations of the elements and the integral characteristics of the whole network open the way to detect the size of synchronous clusters in the neural networks of the epileptic brain before and during seizure.
The data transmission method using the highest harmonics of semiconductor superlattice-based microwave generator has been proposed for biomedical applications. Semiconductor superlattice operated in charge domain formation regime is characterized by the rich high-harmonics power spectrum. The numerical modeling of modulation and detection of the THz range signals using the highest harmonics of the fundamental frequency of the superlattice-based generator was carried out. We have shown effectiveness of the proposed method and discussed the possible applications.
The competition of homophily and homeostasis mechanisms taking place in the multilayer network where several layers of connection topologies are simultaneously present as well as the interaction between layers is considered. We have shown that the competition of homophily and homeostasis leads in such networks to the formation of synchronous patterns within the different layers of the network, which may be both the distinct and identical.
KEYWORDS: Neural networks, Oscillators, Hemodynamics, Chemical elements, Social networks, Solids, Basic research, Biological research, Chemical analysis, Biology, Internet
In the present paper the mechanism of the global synchronization onset through the formation of the synchronous clusters in complex networks with different topologies of links (scale-free networks, small-world networks, random networks) is studied. We consider the dependencies of integral characteristics of synchronous dynamics (synchronization measure, number of synchronous clusters, etc) on coupling strength between nodes. As a basic element of the node oscillator we consider Kuramoto phase oscillator.
We investigate effects of a linear resonator on spatial electron dynamics in semiconductor superlattice. We have shown that coupling the external resonant system to superlattice leads to occurrence of the additional area of negative differential conductance on the current-voltage characteristic, which does not occur in autonomous system. Furthermore, this region shows great increase of generation frequency, that contains practical interest.
This paper is devoted to the analysis of topological changes in complex networks that are reflected in the macroscopic characteristics. We consider a model of the complex network with the adaptive links, in which the synchronous dynamics leads to the appearance of clusters of strongly coupled elements and show that structural changes significantly affect the macroscopic dynamics. As the result, we demonstrate a high possibility of cluster formation in the network that can be analyzed via the consideration of macroscopic characteristics. We also discuss a prospective application for the detection of structural features of neural networks.
In this paper we study mechanisms of the phase synchronization in a model network of Van der Pol oscillators and in the neural network of the brain by consideration of macroscopic parameters of these networks. As the macroscopic characteristics of the model network we consider a summary signal produced by oscillators. Similar to the model simulations, we study EEG signals reflecting the macroscopic dynamics of neural network. We show that the appearance of the phase synchronization leads to an increased peak in the wavelet spectrum related to the dynamics of synchronized oscillators. The observed correlation between the phase relations of individual elements and the macroscopic characteristics of the whole network provides a way to detect phase synchronization in the neural networks in the cases of normal and pathological activity.
We study effects of the external tilted magnetic field on the generation of sub-THz/THz oscillations in the semiconductor superlattice. We show that this field provides the increased power of harmonics in the THz range. Changing the tilt angle essentially influences the distribution of spectral power of current oscillations in the semiconductor superlattice.
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