Synchronizability of Multilayer Networks With K-nearest-neighbor Topologies

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.