Asymptotical state synchronization for the controlled directed complex dynamic network via links dynamics

Abstract From the perspective of large-scale system, a directed complex dynamic network (DCDN) may be considered as a coupling system of the node subsystem (NS) and the link subsystem (LS). In this paper, by using the outgoing link vector and incoming link vector for DCDN, the dynamics of LS is described by employing the vector differential equation instead of the matrix differential equation. Since the outgoing and incoming link vectors have the stronger geometric intuition, the results in this paper show that this kind model of links can not only reflect the direction of links but also find the dynamic tracking goal of links more easily when the state synchronization of NS emerges. Furthermore, by employing the simple mathematical conditions, the nonlinear controller of NS and the coupling term of LS are proposed to ensure achieving the asymptotical state synchronization for DCDN. Finally, the numerical simulations are given to demonstrate the validity of the results in this paper.