Fixed‐time synchronization of stochastic complex networks with Markov jump and mixed delays via adaptive non‐chattering control

Abstract

AbstractIn this article, the fixed‐time synchronization problem for stochastic complex networks (CNs) with Markov jump and mixed delays is investigated. Compared with fixed‐time synchronization of stochastic CNs in existing literature, the fixed‐time synchronization for stochastic CNs with Markov jump and mixed delays is studied for the first time, which is of better significance. Utilizing the Lyapunov method, under the framework of adaptive non‐chattering control, some fixed‐time synchronization conditions are derived. Besides, from the results of the convergence time, the convergence time obtained by the fixed‐time synchronization studied in this article does not depend on the initial value of the system, but is only related to the control parameters. Eventually, a numerical example is also carried out to demonstrate the practicability and validity of our proposed results. Furthermore, a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results.