Synchronizability of Multilayer Networks With K-nearest-neighbor Topologies

Zhang, Li; Wu, Yongqing

doi:10.3389/fphy.2020.571507

Cited by 10 publications

(3 citation statements)

References 34 publications

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“…where x k i is the state of a node, tanh(x k i ) denotes the inherent nonlinear dynamics of the node, i = 1, 2, • • • , 8, k = 1, 2; a ij represents intra-layer connection, and the connection weight is 2; b ij denotes inter-layer connection, and the connection weight is 1. The initial value of the system is randomly selected, X 0 = [−2, 4, −6, 8, −10, 12, −14, 16,10,12,14,16,18,20,22,24]. Through the simulation, the state trajectory of the system is shown in Figures 4 and 5.…”

Section: Numerical Simulation Experiments and Analysismentioning

confidence: 99%

“…The synchronization problem is a significant research topic of complex networks that are often related with phenomena in the real world, such as applause synchronization during performance, simultaneous flicker of fireflies and UAV formation synchronization, and the synchronization-related problems are also an interdisciplinary research topic which may include physics, biology, engineering technology and social science, etc. There exist lots of good research works on the synchronization of the usual single-layer networks, and the results of multi-layer networks that are closer to the actual situation [21][22][23] are relatively few. Li et al [21] compared the size relationships of the synchronizability of two kinds of double-layer dumbbell networks under different coupling modes between layers when the synchronization domain is bounded and unbounded, and verified that the coupling between key nodes between layers has a significant impact on the synchronizability of double-layer dumbbell networks.…”

Section: Introductionmentioning

confidence: 99%

“…Li et al [21] compared the size relationships of the synchronizability of two kinds of double-layer dumbbell networks under different coupling modes between layers when the synchronization domain is bounded and unbounded, and verified that the coupling between key nodes between layers has a significant impact on the synchronizability of double-layer dumbbell networks. Zhang et al [22] gave the analytical expression of the supra-Laplacian matrix of multi-layer K-neighbor networks and analyzed the influence of various parameters on the synchronizability of multi-layer K-neighbor networks in the case of unbounded and bounded synchronization domain. Wang et al [23] studied the synchronization of multi-layer fully coupled networks and analyzed the key factors affecting the synchronizability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

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The system model on synchronizability problem of complex networks with multi-layer structure is closer to the real network than the usual single-layer case. Based on the master stability equation (MSF), this paper studies the eigenvalue spectrum of two k-layer variable coupling windmill-type networks. In the case of bounded and unbounded synchronization domain, the relationships between the synchronizability of the layered windmill-type networks and network parameters, such as the numbers of nodes and layers, inter-layers coupling strength, are studied. The simulation of the synchronizability of the layered windmill-type networks are given, and they verify the theoretical results well. Finally, the optimization schemes of the synchronizability are given from the perspective of single-layer and multi-layer networks, and it was found that the synchronizability of the layered windmill-type networks can be improved by changing the parameters appropriately.

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Section: Numerical Simulation Experiments and Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

et al. 2021

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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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Network coherence of weighted duplex networks: Exact results

Wang

Chen

Sun

2022

Int. J. Mod. Phys. C

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The Laplacian spectra are often used to characterize topological properties and dynamical characteristics of the networks. In this paper, we analytically calculate the network coherence quantified by the Laplacian spectra, which is a measurement of the extent of consensus in the coupled systems with the noise. Due to complex interactions between two coupled networks, we choose three types of weighted duplex networks with an aim of obtaining their exact solutions of the network coherence. Based on the network structures and matrix theories, we provide analytical expressions of the coherence regarding the network size and weights and further study the robustness of the coherence under network parameters. We finally show that smaller network sizes and larger weights will lead to better coherence and the best coherence happens in a duplex network because there are more connections between the layers.

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Synchronizability of Multilayer Networks With K-nearest-neighbor Topologies

Cited by 10 publications

References 34 publications

Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

Synchronizability of Multi-Layer Variable Coupling Windmill-Type Networks

The Laplacian spectrum of weighted composite networks and the applications

Network coherence of weighted duplex networks: Exact results

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