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The mean square synchronization problem of the complex dynamical network (CDN) with the stochastic link dynamics is investigated. In contrast to previous literature, the CDN considered in this paper can be viewed as consisting of two subsystems coupled to each other. One subsystem consists of all nodes, referred to as the nodes subsystem, and the other consists of all links, referred to as the network topology subsystem, where the weighted values can quantitatively reflect changes in the network's topology. Based on the above understanding of CDN, two vector stochastic differential equations with Brownian motion are used to model the dynamic behaviors of nodes and links, respectively. The control strategy incorporates not only the controller in the nodes but also the coupling term in the links, through which the CDN is synchronized in the mean-square sense. Meanwhile, the dynamic stochastic signal is proposed in this paper, which is regarded as the auxiliary reference tracking target of links, such that the links can track the reference target asymptotically when synchronization occurs in nodes. This implies that the eventual topological structure of CDN is stochastic. Finally, a comparison simulation example confirms the superiority of the control strategy in this paper. [ABSTRACT FROM AUTHOR]

This paper formulates and solves a new problem of the double model following adaptive control (MFAC) of nodes and links in a complex dynamical network (CDN). This is different from most existing studies on CDN and MFAC. Inspired by the concept of composite systems, the CDN with dynamic links is regarded as an interconnected system composed of an interconnected node group (NG) and link group (LG). Guided by the above-mentioned new idea of viewing a CDN from the perspective of composite systems, by means of Lyapunov theory and proposed related mathematical preliminaries, a new adaptive control scheme is proposed for NG. In addition, to remove the restriction that the states of links in a CDN are unavailable due to physical constraints, technical restraints, and expensive measurement costs, we synthesize the coupling term in LG with the proposed adaptive control scheme for NG, such that the problem of double MFAC of nodes and links in CDN is solved. Finally, a simulation example is presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]