Synchronization of Stochastic Multilayer Networks by Finite-Time Controller.

It is well known that complex networks are inevitably affected by random disturbances. In the study of complex network stability, finite-time control has always been a research hot spot. This paper discuss finite-time synchronization (FTSY) of stochastic multilayer networks (MLNs). First, novel finite-time stability (FTST) theorems of deterministic complex dynamical system are given, and the expression of finite stability time is also estimated. Second, sufficient criteria are obtained for FTSY of stochastic MLNs. Compared with some the existing research results of FTSY in stochastic MLNs, FTSY of stochastic MLNs is realized by using FTST of deterministic complex dynamical systems, and the relationship between control intensity and network layers is also discussed under the condition of minimum convergence time, which will be meaningful to help how to select appropriate in actual complex system control. Lastly, the availability of the method is checked by numerical simulation base on the theory proposed in this paper.