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.

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.

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.