Macroscopic chimeralike behavior in a multiplex network

Abstract

In this paper we study the dynamics of a multiplex multilayer network, where each layer is composed of identical Kuramoto-Sakaguchi phase oscillators with nonlocal coupling. We focus on a three-layer multiplex network and observe a specific form of multiplex network behavior, the macroscopic chimeralike state. It is decomposed by a splitting of the layers with initially close dynamics into subgroups. The first group consists of two layers performing one type of dynamics, whereas the rest perform the other type, after the introduction of interlayer coupling. Based on an intensive computational analysis, we show that areas of macroscopic chimeralike states are observed close to the critical transition points of intralayer (microscopic) states in the parameter space. We find that this macroscopic chimeralike state is excited at weak and medium interlayer coupling strength, wherein the interlayer phase lag here plays an important role, since this is a network parameter which controls macroscopic dynamics and transforms boundaries between intralayer states. The obtained numerical results are validated analytically by considering the multiplex network dynamics using the Ott-Antonsen reduction of the governing network equations.

Explosive synchronization in interlayer phase-shifted Kuramoto oscillators on multiplex networks

“…Notably, few works have taken the same model as ours but with identical oscillators; they have shown the presence of chimera states due to a phase shift in the intra or interlayer couplings. 34,35 In this work, we show that a phase shift in the interlayer coupling terms of a multiplex network of the Kuramoto oscillators can trigger ES in the layers. Sec.…”

Relay Synchronization in a Weighted Triplex Network

“…Synchronization [11][12][13][14][15] is one among them. Different types of synchronization scenarios have been observed in multiplex framework, such as intra-layer synchronization [16,17], inter-layer synchronization [18][19][20], cluster synchronization [21,22], explosive synchronization [23][24][25], and chimera states [26][27][28].…”

The Multiplex Decomposition: An Analytic Framework for Multilayer Dynamical Networks

“…Various forms of synchronization patterns have been described such as complete [32,90,82], cluster [33], intralayer [71], interlayer [50], and relay synchronization [35,49,79,78,94,81]. It was shown how the interaction of two layers can be used to induce and control certain types of dynamical phenomena such as phase cluster states [11], solitary [53] and chimera states [37,52,60,62,76,77], explosive synchronization [98], congestion [85], stochastic and coherence resonance [80,95]. Recently, intimate relations between adaptive and multilayered coupling structures have been elucidated [12,9,10,44,43,67].…”