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

Recently, the study of random ordinary differential systems, which are driven by second-order moment processes rather than Brownian motion, has attracted increasing attention. This paper investigates the random reaction-diffusion neural networks (RRDNNs) with time-varying delay. The boundary stabilisation of the system is investigated under reasonable assumptions. Stability criteria for ensuring asymptotic stability under the designed controller are derived and the effect of system parameters and time delay on stability is analysed. Additionally, under milder conditions, the noise-to-state stability (NSS) of the system with a boundary controller is discussed, and condition that guarantees NSS for time-delay systems is established. This work represents a pioneering effort in the study of random nonlinear systems within the domain of partial differential equations, particularly focusing on time-delay reaction-diffusion equations. Finally, numerical simulations are conducted to validate the theoretical results.