Synchronizability of two-layer networks

Xu, Mingming; Zhou, Jin; Lu, Jun-an; Wu, Xiaoqun

doi:10.1140/epjb/e2015-60330-0

Cited by 48 publications

(23 citation statements)

References 17 publications

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“…4. It shows that the global epidemic thresholds are always lower than those of the corresponding isolated layers, as indicated by the inequalities (10), (11), and (12). This observation verifies that cooperative epidemic spreading on an interconnected network promotes propagation.…”

Section: A For the Randomly-correlated Homogeneous Networksupporting

confidence: 59%

Cooperative Epidemic Spreading on a Two-Layered Interconnected Network

Xiang¹,

Wu²,

Chen³

et al. 2018

SIAM J. Appl. Dyn. Syst.

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This study is concerned with the dynamical behaviors of epidemic spreading over a two-layered interconnected network. Three models in different levels are proposed to describe cooperative spreading processes over the interconnected network, wherein the disease in one network can spread to the other. Theoretical analysis is provided for each model to reveal that the global epidemic threshold in the interconnected network is not larger than the epidemic thresholds for the two isolated layered networks. In particular, in an interconnected homogenous network, detailed theoretical analysis is presented, which allows quick and accurate calculations of the global epidemic threshold. Moreover, in an interconnected heterogeneous network with inter-layer correlation between node degrees, it is found that the inter-layer correlation coefficient has little impact on the epidemic threshold, but has significant impact on the total prevalence. Simulations further verify the analytical results, showing that cooperative epidemic processes promote the spreading of diseases.Recent works have shown that correlated multiplexity is ubiquitous in the world trade system [20], as well as in transportation network systems [21,22]. Due to their impact on network robustness [21,23] and percolation properties [19,24], multiplex networks has been extensively studied. In [25], the impact of inter-layer correlations on epidemic processes was studied regarding awareness in disease networks. With a degree correlation between double-layer random awareness networks and disease spreading, there is a strong evidence that an epidemic can be suppressed through large-degree nodes arXiv:1702.03926v1 [physics.soc-ph]

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Section: A For the Randomly-correlated Homogeneous Networksupporting

confidence: 59%

Cooperative Epidemic Spreading on a Two-Layered Interconnected Network

Xiang¹,

Wu²,

Chen³

et al. 2018

SIAM J. Appl. Dyn. Syst.

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“…Xu et al. [29] investigated the synchronizability of two-layer networks for three specific coupling patterns, and determined that there exists an optimal value of the inter-layer coupling strength for maximizing complete synchronization in the two-layer networks they analyze. Li et al [30] investigated the sychronizability of a duplex network composed of two star networks with two inter-layer links by giving an analytical expression containing the largest and the smallest nonzero eigenvalues of the Laplacian matrix, the link weight, as well as the network size.…”

Section: Introductionmentioning

confidence: 99%

Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators

et al. 2019

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Synchronization phenomena are of broad interest across disciplines and increasingly of interest in a multiplex network setting. Here we show how the Master Stability Function, a celebrated framework for analyzing synchronization on a single network, can be extended to certain classes of multiplex networks with different intra-layer and inter-layer coupling functions. We derive three master stability equations that determine respectively the necessary regions of complete synchronization, intra-layer synchronization and inter-layer synchronization. We calculate these three regions explicitly for the case of a two-layer network of Rössler oscillators and show that the overlap of the regions determines the type of synchronization achieved. In particular, if the inter-or intra-layer coupling function is such that the inter-layer or intra-layer synchronization region is empty, complete synchronization cannot be achieved regardless of the coupling strength. Furthermore, for any given nodal dynamics and network structure, the occurrence of intra-layer and inter-layer synchronization depend mainly on the coupling functions of nodes within a layer and across layers, respectively. Our mathematical analysis requires that the intraand inter-layer supra-Laplacians commute. But we show this is only a sufficient, and not necessary, condition and that the results can be applied more generally.

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“…In 2014, Aguirre et al discussed the eigenvalue spectrum of two completely identical star networks coupled by an edge between layers [27] and considered synchronizability with different coupling modes between layers. In 2016, Xu et al studied the eigenvalue spectrum and synchronizability of the two-layer star network and theoretically provided the analytic value of the eigenvalue spectrum of the two-layer star network with full connection between layers [28,29]. In 2017, Li et al investigated some rules and properties about synchronizability of duplex networks composed of two networks interconnected by two links, for a specific duplex network composed of two star networks, analytical expressions containing the largest and smallest nonzero eigenvalues of the (weighted) Laplacian matrix, and the interlink weight, as well as the network size, which are given for three different interlayer connection patterns [30].…”

Section: Introductionmentioning

confidence: 99%

Synchronizability of Multilayer Star and Star-Ring Networks

Deng

Jia

Yang

2020

Discrete Dynamics in Nature and Society

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Synchronization of multilayer complex networks is one of the important frontier issues in network science. In this paper, we strictly derived the analytic expressions of the eigenvalue spectrum of multilayer star and star-ring networks and analyzed the synchronizability of these two networks by using the master stability function (MSF) theory. In particular, we investigated the synchronizability of the networks under different interlayer coupling strength, and the relationship between the synchronizability and structural parameters of the networks (i.e., the number of nodes, intralayer and interlayer coupling strengths, and the number of layers) is discussed. Finally, numerical simulations demonstrated the validity of the theoretical results.

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Synchronizability of two-layer networks

Cited by 48 publications

References 17 publications

Cooperative Epidemic Spreading on a Two-Layered Interconnected Network

Cooperative Epidemic Spreading on a Two-Layered Interconnected Network

Master stability functions for complete, intralayer, and interlayer synchronization in multiplex networks of coupled Rössler oscillators

Synchronizability of Multilayer Star and Star-Ring Networks

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