Abstract
In the research on complex networks, synchronizability is a significant measurement of network nature. Several research studies center around the synchronizability of single-layer complex networks and few studies on the synchronizability of multi-layer networks. Firstly, this paper calculates the Laplacian spectrum of multi-layer dual-center coupled star networks and multi-layer dual-center coupled star–ring networks according to the master stability function (MSF) and obtains important indicators reflecting the synchronizability of the above two network structures. Secondly, it discusses the relationships among synchronizability and various parameters, and numerical simulations are given to illustrate the effectiveness of the theoretical results. Finally, it is found that the two sorts of networks studied in this paper are of the same synchronizability, and compared with that of a single-center network structure, the synchronizability of two dual-center structures is relatively weaker.
Highlights
In recent years, the multi-layer complex networks have been applied in many fields, such as communication networks, coupled financial networks, transportation networks, power networks, and social networks [1, 2]
According to the master stability function (MSF), we study the synchronizability of networks under the background of two synchronous regions
Considering the above cases, we found that the synchronizability M ↑ of the two sorts of networks is the same
Summary
The multi-layer complex networks have been applied in many fields, such as communication networks, coupled financial networks, transportation networks, power networks, and social networks [1, 2]. If a leaf node fails working, the network will not be paralyzed These good properties of star structures attracted attention of many researchers. Xu et al studied the relationships among the synchronizability of two-layer star networks and parameters in the case of the unbounded and bounded synchronous regions [27]. Deng et al compared the synchronizability of single-center three-layer star–ring networks and discussed the relationships among the parameters in the case of the unbounded and bounded synchronous regions [29].
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