Fixed-time synchronization of delayed complex dynamical systems with stochastic perturbation via impulsive pinning control

•This paper deals with the fixed time stability of delayed complex dynamical networks system with stochastic perturbations.•I mpulsive pinning controllers are adopted to study the problems, which can save more energy and reduce control costs.•By applying the theory of impulsive control and fixed time stability, novel differential inequalities are established. In this paper, the problem of fixed-time synchronization is investigated for a class of delayed complex dynamical systems with stochastic perturbation. Novel impulsive pinning controllers are proposed for the complex networks to be stochastic fixed-time synchronization in probability. Time delays, stochastic perturbation and impulsive control schemes are all taken into consideration, which make the model more general. The fixed-time synchronization is carried out based on impulsive control technique and stochastic analysis method. Sufficient conditions are proposed to ensure the fixed-time synchronization of the error systems of the stochastic complex dynamical networks. In addition, the settling time function is estimated, which is independent on the initial value. An example is given to illustrate the effectiveness of the theoretical results.