Structural balance control of outgoing links for complex dynamic networks with controlled nodes

From the perspective of large-scale dynamic systems, complex dynamic networks(CDNs) can be considered as coupled by the nodes subsystem(NS) and links subsystem(LS). In this paper, the dynamical model of LS is represented by differential equations about the outgoing links vectors instead of the Riccati matrix differential equations. Since the representation method of vector differential equation has more flexible mathematical properties and geometrical characteristics than the matrix differential equation. In this paper, by designing the controller of NS, with the help of the coupling term for LS, the LS in CDNs asymptotically achieve structural balance. Finally, the effectiveness of the proposed method is verified by the numerical simulation of Hopfield neural network.