A new method for exponential stability of coupled reaction-diffusion systems with mixed delays: Combining Razumikhin method with graph theory

This paper is concerned with a new method for exponential stability of coupled reaction-diffusion systems with mixed delays (CRDSMD). In CRDSMD, the features of reaction-diffusion systems and mixed delays systems are both taken into account. Based on the Razumikhin method and graph theory, several stability conditions are presented, including the Razumikhin-type theorem, the Lyapunov-type theorem and a sufficient criterion in the form of coefficient. As a subsequent result, the coupled reaction-diffusion systems with discrete time-varying delay are also discussed, and a sufficient criterion in the form of coefficient is given to determine its exponential stability. Finally, a numerical example is provided to illustrate the effectiveness of the results developed.