Adaptive synchronization of stochastic complex dynamical networks and its application

This paper investigates exponential synchronization for stochastic complex dynamical networks with reaction–diffusion terms and S-type distributed delays. Based on a generalized Halanay inequality and Poincaré inequality, adaptive control strategies for exponential synchronization are established by constructing a simple Lyapunov–Krasovskii functional candidate and utilizing the truncation method. Some numerical examples are provided to demonstrate the effectiveness of the obtained results. Finally, the proposed adaptive synchronization theoretical results are successfully applied to image encryption.