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. (c) 2021 Elsevier
B.V. All rights reserved.
