Counterpart synchronization of duplex networks with delayed nodes and noise perturbation. (13th November 2015)

• Record Type: Journal Article
• Authors: Wei, Xiang; Wu, Xiaoqun; Lu, Jun-an; Zhao, Junchan
• Is Part Of: Journal of statistical mechanics. (2015:Nov.)
• Publication Date: 2015-11-13
• Subjects: 11 -- 12; 11/060 -- 12/070 -- 11/075; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/2015/11/P11021
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: In the real world, many complex systems are represented not by single networks but rather by sets of interdependent ones. In these specific networks, nodes in one network mutually interact with nodes in other networks. This paper focuses on a simple representative case of two-layer networks (the so-called duplex networks) with unidirectional inter-layer couplings. That is, each node in one network depends on a counterpart in the other network. Accordingly, the former network is called the response layer and the latter network is the drive layer. Specifically, synchronization between each node in the drive layer and its counterpart in the response layer (counterpart synchronization (CS)) in these kinds of duplex networks with delayed nodes and noise perturbation is investigated. Based on the LaSalle-type invariance principle, a control technique is proposed and a sufficient condition is developed for realizing CS of duplex networks. Furthermore, two corollaries are derived as special cases. In addition, node dynamics within each layer can be varied and topologies of the two layers are not necessarily identical. Therefore, the proposed synchronization method can be applied to a wide range of multiplex networks. Numerical examples are provided to illustrate the feasibility and effectiveness of the results.