Prescribed-Time Mean-Square Synchronization of Stochastic Coupled Inertial Neural Networks with Time Delays via Pinning Control

This paper investigates the issue of prescribed-time mean-square synchronization (PTMSS) for stochastic coupled inertial neural networks (SCINNs), encompassing both scenarios without time delays (TDs) and with TDs. By constructing appropriate Lyapunov functionals and utilizing the prescribed-time stability (PTS) approach, combined with the theory of directed spanning trees, several sufficient conditions are rigorously derived to realize the prescribed-time mean-square synchronization within a given time $t_p$ for SCINNs with and without TDs. Different from most existing results that primarily address deterministic systems or neglect stochastic disturbances and time delays, this work explicitly takes into account both stochastic disturbances and TDs, thereby enhancing the model's practical applicability. Moreover, two categories of pinning controllers are devised, which greatly improve control efficiency. Finally, numerical simulations are conducted to validate the theoretical results and demonstrate the effectiveness of the proposed control strategies.