Mikhail V. Goremyko

Excitation and suppression of chimeric states in the multilayer network of oscillators with nonlocal coupling

The interaction between ensembles of coupled nonlinear oscillators using the model of multilayer network is studied. It is found that the interaction between an ensemble with a chimera and an ensemble with both coherent and incoherent states of oscillators can lead to both suppression of the chimera and a transition to a coherent or incoherent state, or to the excitation of the chimeric state from the coherent or incoherent state, respectively.

Interaction of chimera states in a multilayered network of nonlocally coupled oscillators

The processes of formation and evolution of chimera states in the model of a multilayered network of nonlinear elements with complex coupling topology are studied. A two-layered network of nonlocally intralayer-coupled Kuramoto–Sakaguchi phase oscillators is taken as the object of investigation. Different modes implemented in this system upon variation of the degree of interlayer interaction are demonstrated.

Interplay between geo-population factors and hierarchy of cities in multilayer urban networks

Only taking into consideration the interplay between processes occurring at different levels of a country can provide the complete social and geopolitical plot of its urban system. We study the interaction of the administrative structure and the geographical connectivity between cities with the help of a multiplex network approach. We found that a spatially-distributed geo-network imposes its own ranking to the hierarchical administrative network, while the latter redistributes the shortest paths between nodes in the geographical layer. Using both real demographic data of population censuses of the Republic of Kazakhstan and theoretical models, we show that in a country-scale urban network and for each specific city, the geographical neighbouring with highly populated areas is more important than its political setting. Furthermore, the structure of political subordination is instead crucial for the wealth of transportation network and communication between populated regions of the country.

Numerical analysis of the chimera states in the multilayered network model

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

Self-organization in multilayer network with adaptation mechanisms based on competition

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.

Nonlinear dynamics of the complex multi-scale network

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.

Study of the interactions in neural ensemble of the brain using wavelet analysis

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.

Study of pattern formation in multilayer adaptive network of phase oscillators in application to brain dynamics analysis

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.

Numerical and analytical investigation of the chimera state excitation conditions in the Kuramoto-Sakaguchi oscillator network

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.

Pattern formation in adaptive multiplex network in application to analysis of the complex structure of neuronal network of the brain

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.