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.
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.
We consider competition between layers in adaptive multiplex networks of phase oscillators, where adaptation principles (which cause intra-layer topology evolution) are inspired by real world homophily and homeostasis phenomena. Our model yields the emergence of both scale-free topologies and meso-scale structures in the layers, for an appropriate choice of the control parameters. We further report that the growth of the number of interacting layers leads to a decrease of the global order, due to inter-layer structural competition. However, the increase of the system's scale can effect local synchronization between neighboring (or strongly coupled) nodes. Such unforeseen phenomena is connected with the nature of the competitive mechanism, which implies the rivalry for optimal structure within the whole system, a situation occurring in a variety of natural systems.
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