Abstract
In this paper, the synchronizability of multilayer K-nearest-neighbor networks is studied by using the master stability function method. The analytical expressions for the eigenvalues of the supra-Laplacian matrix are given for two-layer and multilayer K-nearest-neighbor networks. In addition, the impacts of various topological parameters (such as the network size, the node degree, the number of layers, the intra-layer and the inter-layer coupling strengths) on the network synchronizability are discussed. Finally, the theoretical results are verified through numerical simulation.
Highlights
Since the appearance of small-world networks and scale-free networks [1, 2], complex networks have attracted much attention due to their pervading through various scientific fields
Tang et al proposed three necessary regions to describe the different types of coherent behaviors in multiplex networks based on the master stability function method [25]
Motivated by the above discussion, we study the synchronizability of multilayer networks with K-nearestneighbor topologies
Summary
Since the appearance of small-world networks and scale-free networks [1, 2], complex networks have attracted much attention due to their pervading through various scientific fields. Most of the existing works focused on the effects of network structures on the synchronizability of multilayer networks through numerical simulation. The present study uses the master stability function method to investigate the relationships between various topological parameters and network synchronizability. With this framework, we strictly derive the analytical expressions for the eigenvalues of two-layer and multilayer K-nearest-neighbor networks. Analytical and numerical results show that the network size, the node degree, the number of layers, the intra-layer and the inter-layer coupling strengths can have important effects on the synchronizability of multilayer K-nearest-neighbor networks.
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