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In this article, a delayed reaction-diffusion predator-prey model with stage structure is investigated. The global stability of the coexistence states is discussed by the linearization method and the method of upper and lower solutions. Sufficient conditions of the global attractivity of nonnegative constant equilibrium of the system are obtained. Our results show that the free diffusion of the delayed reactiondiffusion system has no influence on the populations. Finally, numerical simulations are carried out to illustrate the main results. Keywords—reaction-diffusion; time delay; the method of upper and lower solutions; global stability

The Global Stability of a Delayed Reaction-Diffusion Predator-Prey Model