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Keywords = supra-Laplacian matrix

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16 pages, 753 KiB  
Article
Synchronizability of Multilayer Directed Dutch Windmill Networks
by Yongqing Wu and Xiao Zhang
Fractal Fract. 2022, 6(10), 537; https://doi.org/10.3390/fractalfract6100537 - 23 Sep 2022
Cited by 5 | Viewed by 1641
Abstract
This paper investigates the synchronizability of multilayer directed Dutch windmill networks with the help of the master stability function method. Here, we propose three types of multilayer directed networks with different linking patterns, namely, inter-layer directed networks (Networks-A), intra-layer directed networks (Networks-B), and [...] Read more.
This paper investigates the synchronizability of multilayer directed Dutch windmill networks with the help of the master stability function method. Here, we propose three types of multilayer directed networks with different linking patterns, namely, inter-layer directed networks (Networks-A), intra-layer directed networks (Networks-B), and hybrid directed networks (Networks-C), and rigorously derive the analytical expressions of the eigenvalue spectrum on the basis of their supra-Laplacian matrix. It is found that network structure parameters (such as the number of layers and nodes, the intra-layer and the inter-layer coupling strengths) have a significant impact on the synchronizability in the case of the two typical synchronized regions. Finally, in order to confirm that the theoretical conclusions are correct, simulation experiments of multilayer directed network are delivered. Full article
(This article belongs to the Special Issue Fractional-Order Chaotic System: Control and Synchronization)
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16 pages, 2834 KiB  
Article
Synchronizability of Multi-Layer-Coupled Star-Composed Networks
by Haiping Gao, Jian Zhu, Xianyong Li and Xing Chen
Symmetry 2021, 13(11), 2224; https://doi.org/10.3390/sym13112224 - 21 Nov 2021
Cited by 3 | Viewed by 1899
Abstract
In this paper, several multi-layer-coupled star-composed networks with similar symmetrical structures are defined by using the theory of graph operation. The supra-Laplacian matrix of the corresponding multi-layer networks is obtained according to the master stability equation (MSF). Two important indexes that reflect the [...] Read more.
In this paper, several multi-layer-coupled star-composed networks with similar symmetrical structures are defined by using the theory of graph operation. The supra-Laplacian matrix of the corresponding multi-layer networks is obtained according to the master stability equation (MSF). Two important indexes that reflect the synchronizability of these kinds of networks are derived in the case of bounded and unbounded synchronized regions. The relationships among the synchronizability, the number of layers, the length of the paths, the branchings, and the interlayer and intralayer coupling strengths in the two cases are studied. At the same time, the simulation experiments are carried out with the MATLAB software, and the simulated images of the two symmetrical structure networks’ synchronizability are compared. Finally, the factors affecting the synchronizability of multi-layer-coupled star-composed networks are found. On this basis, optimization schemes are given to improve the synchronizability of multi-layer-coupled star-composed networks and the influences of the number of central nodes on the networks’ synchronizability are further studied. Full article
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