Mean field phase synchronization between chimera states

Abstract

We study two-layer networks of identical phase oscillators. Each individual layer is a ring network for which a non-local intra-layer coupling leads to the formation of a chimera state. The number of oscillators and their natural frequencies is in general different across the layers. We couple the phases of individual oscillators in one layer to the phase of the mean field of the other layer. This coupling from the mean field to individual oscillators is done in both directions. For a sufficient strength of this inter-layer coupling, the phases of the mean fields lock across the two layers. In contrast, both layers continue to exhibit chimera states with no locking between the phases of individual oscillators across layers, and the two mean field amplitudes remain uncorrelated. Hence, the networks' mean fields show phase synchronization which is analogous to the one between low-dimensional chaotic oscillators. The required coupling strength to achieve this mean field phase synchronization increases with the mismatches in the network sizes and the oscillators' natural frequencies.

Remote pacemaker control of chimera states in multilayer networks of neurons

“…Recently, a prominent line of research emerged which studies chimera states in multilayer networks [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Multilayer networks are important modelling tools for complex systems such as transportation networks, social interactions and the brain [58,59].…”

“…Subsequently, Ref. [50] was the first study on chimera states in a network with layers of different sizes. There the authors modelled a mean field interlayer coupling and observed that the phases of the order parameters of the two layers synchronize [50].…”

“…[50] was the first study on chimera states in a network with layers of different sizes. There the authors modelled a mean field interlayer coupling and observed that the phases of the order parameters of the two layers synchronize [50]. In [49] it was shown that in a multiplex scheme with three layers formed by ring networks of FitzHugh-Nagumo oscillators, time delays can control relay synchronization between chimera states.…”

Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps

“…[61][62][63][64][65][66][67][68] Nowadays, the attention of researchers is focused on the effects that can occur not only in isolated (individual) ensembles but in large systems of interacting ensembles. The interaction between ensembles (layers) in multilayer networks can lead to different types of synchronization of complex spatiotemporal structures, including chimeras, e.g., cluster synchronization, 73,74 complete synchronization, 75 generalized synchronization, 76 phase synchronization, 77 external and mutual synchronization, [78][79][80] explosive synchronization, [81][82][83] etc.…”

Control of Chimera States in Multilayer Networks

“…Current research in the field of complex systems is moving beyond simple network structures to more complicated, realistic topologies. One of them are multilayer networks, which find a wide range of applications in nature and technology, such as neuronal and genetic networks, social networks, power grids, transportation networks [78][79][80][81][82][83][84][85][86][87][88][89][90][91]. Recent studies have been focused on various synchronization scenarios in multilayer structures, including remote and relay synchronization [92][93][94].…”