Counterpart synchronization of duplex networks with delayed nodes and noise perturbation

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