Moment‐based analysis of pinning synchronization in complex networks
Linying Xiang, Yanying Yu, Jiawei Zhu · Asian Journal of Control · 2021
Abstract In this paper, pinning synchronization of complex networks is investigated from a moment‐based analysis approach. The analytical expressions for the first three expected moments of the coupling and control matrix for an ER random graph, a Chung‐Lu random network, and an NW small‐world network are derived, respectively. The shape of the eigenvalue distribution of the coupling and control matrix can be estimated based on the obtained expected moments and thus used to predict pinning synchronization in the network. It is shown that the expected moments are associated with the local structural properties of the network and the control mechanism. This allows us to bound the smallest and largest eigenvalues of the spectral distribution without computing the Laplacian eigenvalues of a large‐scale network. Numerical simulations of the above three representative networks composing of chaotic systems, respectively, are shown for illustration and verification.