In this paper we study the dynamics of a multi-layer network composed of identical layers of non-locally coupled Kuramoto-Sakaguchi phase oscillators. Throughout the intensive numerical study we consider three-layer multiplex network and reveal conditions for a specific form of multi-layer network behavior, the macroscopic chimera-like state. It represents an excitation of different spatiotemporal patterns in initially identical layers of multiplex network under their interaction. Also, we show that transition to such macroscopic chimera patterns can be achieved not only variation of phase shift, but according to introduction of heterogeneity of network elements.
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 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.
We have proposed brain-computer interface (BCI) for the estimation of the brain response on the presented visual tasks. Proposed BCI is based on the EEG recorder Encephalan-EEGR-19/26 (Medicom MTD, Russia) supplemented by a special home-made developed acquisition software. BCI is tested during experimental session while subject is perceiving the bistable visual stimuli and classifying them according to the interpretation. We have subjected the participant to the different external conditions and observed the significant decrease in the response, associated with the perceiving the bistable visual stimuli, during the presence of distraction. Based on the obtained results we have proposed possibility to use of BCI for estimation of the human alertness during solving the tasks required substantial visual attention.
Problem of interaction between human and machine systems through the neuro-interfaces (or brain-computer interfaces) is an urgent task which requires analysis of large amount of neurophysiological EEG data. In present paper we consider the methods of parallel computing as one of the most powerful tools for processing experimental data in real-time with respect to multichannel structure of EEG. In this context we demonstrate the application of parallel computing for the estimation of the spectral properties of multichannel EEG signals, associated with the visual perception. Using CUDA C library we run wavelet-based algorithm on GPUs and show possibility for detection of specific patterns in multichannel set of EEG data in real-time.
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.
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.
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