Adaptive control for complex dynamical networks with structural balance via external stimulus signals

摘要

This paper investigates the adaptive structural balance control of complex dynamical networks by employing the controlled external stimulus signals which are coupled and transmitted to the dynamics of complex dynamical network. The control objective is to assure the asymptotical convergence of the dynamical links to the structural balance by the controlled external stimulus signals. The dynamical links of complex dynamical network are represented in this paper mathematically as the Riccati matrix differential equation with the controlled external stimulus signals which are coupled approximately in the form of Hebb rule. Compared with the existing results which are mainly concerned with the dynamical characteristics of nodes such as synchronization, this paper is mainly focused on the dynamical characteristic of links so named as the structural balance which is asymptotically obtained by the adaptive control scheme of external stimulus signals. Finally, a simulation example is given to show the validity of result proposed in this paper.