Boundary control of random reaction–diffusion neural networks with time-varying delay

Recently, the study of random nonlinear systems driven by second-order moment processes rather than Brownian motion has attracted increasing attention. This paper investigates random reaction–diffusion neural networks with time-varying delay. An integral-type boundary controller is designed, and sufficient conditions are derived to ensure asymptotic stability while revealing the influence of system parameters and time delay on stability. Under weaker assumptions, the noise-to-state stability of the controlled system is further established. This work constitutes an initial attempt to study random systems in a partial differential equation setting, particularly for time-delay reaction–diffusion equations. Finally, numerical simulations are presented to verify the theoretical results.