Achieving exponential synchronization in nonlinear stochastic complex networks with time-varying delays: A pinning impulsive control strategy

This study investigates exponential synchronization for complex networks with nonlinear coupling structures, stochastic perturbations, and hybrid time-varying delays. The proposed model integrates both internal and coupling-induced time-varying delays. A pinning impulsive control strategy is developed to synchronize the network, which only requires partial node intervention. Based on stochastic analysis and Lyapunov stability theory, we rigorously derive sufficient conditions for exponential convergence. The results reveal that synchronizing the entire network requires only limited impulsive control inputs, significantly reducing control costs. Finally, two numerical examples validate the theoretical framework and demonstrate its practical effectiveness.