Abstract
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.
Highlights
Network science is an interdisciplinary subject which abstracts physical, biological, economic and social systems into networks composed of nodes and edges and studies their structural characteristics, dynamic evolution and dynamic characteristics. e network synchronization as an important emerging phenomenon of a population of dynamically interacting units in various fields of science has attracted much attention
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 Laplacian matrix, and the interlink weight, as well as the network size, which are Discrete Dynamics in Nature and Society given for three different interlayer connection patterns [30]
When a > Md, the multilayer star-ring network has the same synchronizability as that of the multilayer star network under taking the same structural parameter values. e synchronizability of the two networks is determined by the number of the layers M and the interlayer coupling strength d between leaf nodes and invariant with increasing N, for the unbounded synchronous region; the synchronizability of the two networks is weakened with increasing N, for the bounded synchronous region. e simulation results are consistent with the theoretical results
Summary
Network science is an interdisciplinary subject which abstracts physical, biological, economic and social systems into networks composed of nodes and edges and studies their structural characteristics, dynamic evolution and dynamic characteristics. e network synchronization as an important emerging phenomenon of a population of dynamically interacting units in various fields of science has attracted much attention. Deng et al studied the problem of synchronization of two kinds of multiplex chain networks under different coupling modes between layers and derived the eigenvalue spectrum of the supraLaplacian matrices of those networks [34]. Due to the structural complexity of multilayer networks, there is almost no strict theoretical derivation on the eigenvalues of the multilayer network; most of the studies are based on the results of numerical simulation on synchronizability of that. To provide more useful foundations for getting insight into understanding synchronizability of multilayer networks and explore the main influencing factors of synchronizability, in our paper, two kinds of typical multilayer networks (i.e., multilayer star and star-ring networks) are considered on the basis of the literature [28] that studied the synchronizability of the two-layer star network; we strictly derived the eigenvalue spectrum of the supra-Laplacian matrices of multilayer star and star-ring networks (not limited to two layers) and studied the relationships between the synchronizability and structural parameters of that.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
