Stability for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays

Abstract

In this paper, the global robust asymptotic stability problem for a class of generalized reaction–diffusion uncertain stochastic neural networks with mixed delays is investigated under Dirichlet boundary conditions and Neumann boundary conditions, respectively. The proposed generalized neural networks model includes reaction–diffusion local field neural networks and reaction–diffusion static neural networks as its special cases. By using stochastic analysis approaches and constructing a suitable Lyapunov–Krasovskii functional, some simple and useful criteria for global robust asymptotic stability of the neural networks are obtained. According to the theoretical results, the influences of diffusion coefficients, diffusion spaces, stochastic perturbation, and uncertain parameters are analyzed. Finally, numerical examples are provided to show the feasibility and efficiency of the proposed methods, and by choosing different diffusion coefficients and diffusion spaces, different stability states can be achieved.