Synchronizability of duplex regular networks

¹ School of Mathematics and Statistics, Wuhan University - Wuhan 430072, China
² Department of Engineering, Honghe University - Honghe 661199, China
³ Research Center of Complex Network, Wuhan University - Wuhan 430072, China
⁴ Hubei Key Laboratory of Computational Science, Wuhan University - Wuhan 430072, China

^(a) xqwu@whu.edu.cn (corresponding author)

Received: 22 October 2017
Accepted: 19 December 2017

Abstract

In this paper, we investigate the synchronizability of duplex regular networks based on the master stability function framework. We study potential factors influencing synchronizability, including the network size, the coupling strength and the inter-layer connection density. From both theoretical and numerical results, we obtain that with the same size, same coupling strength and same inter-layer connection density, duplex fully-connected networks have the best synchronizability, the next is duplex stars, followed by duplex rings, and duplex chain networks have the worst synchronizability. The order of synchronizability on duplex regular networks is similar to that on single networks. We find that synchronizability of duplex regular networks is always worse than that of its isolated layer. Furthermore, for duplex fully-connected or star networks with fixed coupling strength, we find that the more the inter-layer links are, the better the synchronizability is. However, for duplex ring or chain networks, partial inter-layer links can yield the same synchronizability as that caused by one-to-one inter-layer links. Though these findings are obtained by using duplex regular networks, they will provide insight into understanding the synchronizability of general multiplex networks, and facilitate the selection of network parameters for obtaining optimum synchronizability.