Pinning Control of Multiplex Dynamical Networks Using Spectral Graph Theory
利用李雅普诺夫稳定性和谱图理论，研究了多层动态网络的牵制同步问题，建立了图论同步判据，发现层间耦合强度促进层内同步。
Pinning control has been attracting wide attention for the study of various complex networks for decades. This article explores grounded theory on the pinning synchronization of the emerging multiplex dynamical networks. The multiplex dynamical networks under study can describe many real-world scenarios, in which different layers have distinct individual dynamics of node. In this work, we build the bridge between multiplex structures and network dynamics by using the Lyapunov stability theory and the spectral graph theory. Furthermore, by analyzing spectral properties of the grounded super-Laplacian matrices, we set up several graph-based synchronization criteria for multiplex networks via pinning control. In addition, we overcome the difficulties induced by distinct node dynamics in different layers, and find that interlayer coupling strengths promote intralayer synchronization of multiplex networks. Finally, a collection of numerical simulations verifies the effectiveness of theoretical results.