General Decay Synchronization of Multiplex Networks via Delayed Feedback Control

This article addresses general decay synchronization matter for multiplex and directed networks via delayed feedback control. Decay synchronization is regarded as a class of ψ-type synchronization, which derives from the generalizations of ψ-type function and ψ-type stability. By exploiting appropriate nonlinear control positioned on a portion of multiplex networks, synchronization for the network system is solved with decay rate. In comparison with previous multiplex networks, the present model contains asymmetric, with non-cooperative factors and not connected outer matrices, combined with negative elements of inner matrices in the article, which improves existing results well. We propose a synchronization method for multiplex network under this constraint from angle of inner matrices. It is proved that if weighted group of union new matrices for each dimension is strongly connected, then decay synchronization and anti-synchronization can be realized under delayed feedback controller. Moreover, some specific modes for synchronization are illustrated more precisely. In addition, reaction-diffusion systems are also further conducted as an application. Simulations are given for verifying the validity of gained results.