A new method for global stability analysis of delayed reaction-diffusion neural networks

This paper presents improved criteria for global exponential stability of reaction-diffusion neural networks with time-varying delays. A novel diffusion-dependent Lyapunov functional, which is directly linked to the diffusion terms, is suggested to analyze the role of diffusivity of each neuron on the model dynamics. In the case of Dirichlet boundary conditions, the extended Wirtinger's inequality is employed to exploit the stabilizing effect of reaction-diffusion terms. In the framework of descriptor system approach, the augmented Lyapunov functional technique is utilized to reduce the conservatism in the values of the time delay bounds. As a result, the derived global stability criteria are more effective than the existing ones. Three numerical examples are provided to illustrate the effectiveness of the proposed methodology.