Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

Zhu, Jian; Huang, Da; Jiang, Haijun; Bian, Jicheng; Yu, Zhiyong

doi:10.3390/math9212721

Cited by 8 publications

(1 citation statement)

References 28 publications

(38 reference statements)

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“…With the deepening of the research, scholars have found that most complex systems are not isolated, but are instead interdependent and interactive. Researchers introduced the concept of multi-layer networks to describe such networks and have made fruitful achievements in the field of research on multi-layer networks, such as accomplishing the synchronization of multi-layer complex networks [6][7][8][9][10][11][12], structure identification of multi-layer networks [13], and cascading failures and consensus of multi-layer networks [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Robustness of Consensus of Two-Layer Ring Networks

Gao²,

Shang

et al. 2023

Symmetry

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The topology structure of multi-layer networks is highly correlated with the robustness of consensus. This paper investigates the influence of different interlayer edge connection patterns on the consensus of the two-layer ring networks. Two types of two-layer ring network models are first considered: one is a kind of two-layer ring network with two linked edges between layers (Networks-a), and the other is a kind of two-layer ring network with three linked edges between layers (Networks-b). Using the Laplacian spectrum, the consensus of the network model is derived. The simulation experiments are used to demonstrate the influence of different interlayer edge connection patterns on the consensus of networks. To determine the best edge connection pattern for Networks-a and Networks-b, the number of nodes in a single-layer ring network is denoted by n. The best edge connection pattern for Networks-a is 1 & [(n+2)/2]. Furthermore, n is subdivided into 3k,3k+1,3k+2, and the best edge connection patterns of Networks-b are near 1 & k+1 & 2k+1.

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Section: Introductionmentioning

confidence: 99%

Robustness of Consensus of Two-Layer Ring Networks

Gao²,

Shang

et al. 2023

Symmetry

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The Laplacian spectrum of weighted composite networks and the applications

Zhu,

Huang,

Gao

et al. 2024

AIP Advances

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The topological properties of the networks can be described by the Laplacian spectra, but resolving the Laplacian spectra of networks poses difficulties. In this study, a novel approach for solving the Laplacian spectrum of weighted composite networks is presented. We first give the definitions of three weighted graph operations, namely, Cartesian product, corona, and join. Second, the Laplacian spectra of these composite networks are calculated. Finally, we use the obtained Laplacian spectrum to deduce some topological properties of the networks, such as network coherence, entire mean first-passage time, and Laplacian energy, which have several applications in physical chemistry.

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Robustness of synchronizability in windmill networks with node failures

Zhang

Chen

et al. 2022

Int. J. Mod. Phys. B

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In this paper, the synchronizability characterized by the Laplacian spectrum is applied to windmill networks where three types of parameters are introduced to control the number of deleted nodes. Using the network’s structures, exact solutions of the Laplacian eigenvalues are obtained and metrics of the synchronizability are correspondingly shown. Relationships between the synchronizability and the introduced parameters are presented. Then, the synchronizability of models with different settings of node failures is compared. The obtained results reveal distinct synchronizabilities originating from intrinsic structures of models and the setting forms of node failures. Finally, numerical examples are provided to verify the effectiveness of theoretical analysis.

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Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

Cited by 8 publications

References 28 publications

Robustness of Consensus of Two-Layer Ring Networks

Robustness of Consensus of Two-Layer Ring Networks

The Laplacian spectrum of weighted composite networks and the applications

Robustness of synchronizability in windmill networks with node failures

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