Relay synchronization in multiplex networks

Leyva, I.; Sendiña‐Nadal, Irene; Sevilla-Escoboza, R.; Vera-Ávila, V. P.; Chholak, Parth; Boccaletti, Stefano

doi:10.1038/s41598-018-26945-w

Cited by 71 publications

(47 citation statements)

References 59 publications

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“…It is to be noted that even though  follows the connection matrix (2), which indicates that the delayed layer 1 and the un-delayed layer 3 are not directly interconnected, yet, by means of layer 2 that acts as a relay layer, the layer 3 exhibits exactly the same transition type as that of the layer 1. Hence, this is an instance of distant coordination similar to the remote (relay) synchronization in the multiplex networks [26]. On the basis of this finding we can say that for a multiplex network of a finite number of layers, the intra-layer delay introduced in one layer is sufficient to incorporate the same transition behavior in rest of the layers.…”

Section: Effect Of Number Of Multiplexed Layers L On the Transitionmentioning

confidence: 66%

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Delay regulated explosive synchronization in multiplex networks

Kachhvah

Jalan

2019

New J. Phys.

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It is known that explosive synchronization (ES) in an isolated network of Kuramoto oscillators with inertia is significantly enhanced by the presence of time delay. Here we show that time delay in one layer of the multiplex network governs the transition to synchronization and ES in the other layers. We found that a single layer with time-delayed intra-layer coupling may experience a different type of transition to synchronization, e.g. ES or continuous, depending on the values of time delay. Importantly, the same type of transition is incorporated simultaneously in other layer(s) as well, irrespective of the intra-layer delay values. Hence, a suitable choice of time-delay in only one layer of a multiplex network can lead to a desired (either ES or continuous) transition simultaneously in the other layers, either directly or remotely connected to the delayed layer. These results offer a platform for a better understanding of the dynamics of those complex systems which are represented by the multilayered framework and contain time delays in the communication processes.

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Section: Effect Of Number Of Multiplexed Layers L On the Transitionmentioning

confidence: 66%

“…top of the multiplex frameworks [26][27][28][29][30]. Of late, the emergence of ES has been shown in the multilayer networks comprised of Kuramoto oscillators as well as second-order Kuramoto oscillators [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Delay regulated explosive synchronization in multiplex networks

Kachhvah

Jalan

2019

New J. Phys.

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“…A useful measure for synchronization between two layers i, j is given by the global inter-layer synchronization error E ij [14,45]:…”

Section: Relay Synchronizationmentioning

confidence: 99%

Chimeras in Multiplex Networks: Interplay of Inter- and Intra-Layer Delays

Sawicki

Ghosh

Jalan

et al. 2019

Front. Appl. Math. Stat.

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Time delay in complex networks with multiple interacting layers gives rise to special dynamics. We study the scenarios of time delay induced patterns in a three-layer network of FitzHugh-Nagumo oscillators. The topology of each layer is given by a nonlocally coupled ring. For appropriate values of the time delay in the couplings between the nodes, we find chimera states, i.e., hybrid spatio-temporal patterns characterized by coexisting domains with incoherent and coherent dynamics. In particular, we focus on the interplay of time delay in the intra-layer and inter-layer coupling term. In the parameter plane of the two delay times we find regions where chimera states are observed alternating with coherent dynamics. Moreover, in the presence of time delay we detect full and relay inter-layer synchronization.

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“…Of particular interest is the synchronization of chimera states in multicomponent systems and networks. Recently, various synchronization scenarios in multiplex and multilayer [23][24][25][26][27][28][29][30][31] networks were studied, such as generalized synchronization [32], inter-layer (external and mutual) synchronization [33][34][35][36][37][38], relay (remote) synchronization [39,40], explosive synchronization [41][42][43][44]. Among a large variety of chimera states [35,, here we concentrate on so-called "spiral wave chimera structures" which are observed in 2D ensembles of coupled nonlinear oscillators [10,22,[73][74][75][76][77][78][79][80][81][82][83][84][85][86].…”

Section: Introductionmentioning

confidence: 99%

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

Bukh¹,

Strelkova²,

Анищенко³

2019

ISUNSSP

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The paper describes the spatio-temporal dynamics of a lattice that is given by a 2D N × N network of nonlocally coupled Nekorkin maps which model neuronal activity. The network behavior is studied for periodic and no-flux boundary conditions. It is shown that for certain values of the coupling parameters, rotating spiral waves and spiral wave chimeras can be observed in the considered lattice. We analyze and compare statistical and dynamical characteristics of the local oscillators from coherence and incoherence clusters of a spiral wave chimera. Furthermore, effects of mutual and external synchronization of spiral wave structures in two coupled such lattices are studied. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establish the mechanism of their synchronization. Our numerical studies indicate that when the coupling strength between the lattices is sufficiently weak, only a certain part of oscillators of the interacting networks is imperfectly synchronized, while the other part demonstrates a partially synchronous behavior. If the spatiotemporal patterns in the lattices do not include incoherent cores, imperfect synchronization is realized for most oscillators above a certain value of the coupling strength. In the regime of spiral wave chimeras, the imperfect synchronization of all oscillators cannot be achieved even for sufficiently large values of the coupling strength.

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Relay synchronization in multiplex networks

Cited by 71 publications

References 59 publications

Delay regulated explosive synchronization in multiplex networks

Delay regulated explosive synchronization in multiplex networks

Chimeras in Multiplex Networks: Interplay of Inter- and Intra-Layer Delays

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

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