Stability and Robust Stability of Stochastic Reaction–Diffusion Neural Networks With Infinite Discrete and Distributed Delays

This paper investigates the $\phi$ -type stability and robust stability for a general class of stochastic reaction–diffusion neural networks (SRDNNs) with Dirichlet boundary conditions, infinite discrete time-varying delays, and infinite continuously distributed delays. By virtue of inequality techniques, properties of $\boldsymbol M$ -matrix, and theories of stochastic analysis, several sufficient criteria are obtained to guarantee the almost sure $\boldsymbol \phi$ -type stability, $\boldsymbol p$ th moment $\boldsymbol \phi$ -type stability, and $\boldsymbol \phi$ -type robust stability of the underlying SRDNNs with hybrid unbounded time delays. With appropriate choices of the function $\boldsymbol \phi$ , the $\boldsymbol \phi$ -type stability reduces to the exponential stability, polynomial stability, and logarithmic stability. Additionally, the developed results herein include some existing ones as special cases. A numerical simulation is performed to substantiate the effectiveness and superiority of the theoretical analysis.