Estimation of the time cost with pinning control for stochastic complex networks

In this paper, the finite-time and fixed-time stochastic synchronization of complex networks with pinning control are investigated. Considering the time and energy cost of control, combining the advantages of finite-time control technology and pinning control technology, efficient protocols are proposed. Compared with the existing research, the influence of noise is considered, and sufficient conditions for the network to achieve stochastic synchronization in a finite time are given in this paper. Based on the stability theory of stochastic differential equations, the upper bound of the setting time is estimated. Finally, the effects of control parameters, noise intensity, and the number of control agents on the network synchronization rate are studied. Numerical simulations verify the validity and correctness of the theoretical results.