Synchronization of chimera states in a multiplex system of phase oscillators with adaptive couplings

Abstract

We study the interaction of chimera states in multiplex two-layer systems, where each layer represents a network of interacting phase oscillators with adaptive couplings. A feature of this study is the consideration of synchronization processes for a wide range of chimeras with essentially different properties, which are achieved due to the use of different types of coupling adaptation within isolated layers. We study the effect of forced synchronization of chimera states under unidirectional action between layers. This process is accompanied not only by changes in the frequency characteristics of the oscillators, but also by the transformation of the structure of interactions within the slave layer that become close to the properties of the master layer of the system. We show that synchronization close to identical is possible, even in the case of interaction of chimeras with essentially different structural properties (number and size of coherent clusters) formed by means of a relatively large parameter mismatch between the layers. In the case of mutual action of the layers in chimera states, we found a number of new scenarios of the multiplex system behavior along with those already known, when identical or different chimeras appear in both layers. In particular, we have shown that a fairly weak interlayer coupling can lead to suppression of the chimera state when one or both layers of the system demonstrate an incoherent state. On the contrary, a strong interlayer coupling provides a complete synchronization of the layer dynamics, accompanied by the appearance of multicluster states in the system’s layers.

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

“…In the context of neuronal networks, such a multilayer approach is ideal for addressing the relationship between structure and function, an essential question in theoretical neuroscience [59]. Concerning chimera states, studies on multilayer/multiplex networks are limited and mainly deal with artificial coupling schemes [23,[60][61][62][63]. For example, the case of two populations with various coupling schemes has been systematically studied in reference [22].…”

Cloning of Chimera States in a Large Short-term Coupled Multiplex Network of Relaxation Oscillators

“…At present, great attention is paid to studying of interaction of chimera states. The effects of generalized synchronization of chimera states [36], synchronization of chimera states in ensembles with asymmetrical connections [37], synchronization of chimera states in multiplex networks with delays [38], synchronization of chimera states in a two-layer multiplex network with adaptive connections in each layer [39], synchronization of chimera states in modular networks [40,41], interaction of chimera states with fully coherent or fully incoherent states [42], etc. were explored.…”

Desynchronization Transitions in Adaptive Networks

“…Moreover, adaptive networks have been reported for chemical [67,68], epidemic [69], biological [70], transport [71], and social systems [72,73]. A paradigmatic example of adaptively coupled phase oscillators has recently attracted much attention [12,41,[74][75][76][77][78][79][80][81], and it appears to be useful for predicting and describing phenomena in more realistic and detailed models [82][83][84][85]. Systems of phase oscillators are important for understanding synchronization phenomena in a wide range of applications [86][87][88].…”

“…We consider the following general class of N adaptively coupled systems [12,41,[74][75][76][77][78][79][80]89] x…”