Abstract
In this paper, we study a delayed predator-prey reaction-diffusion system with Beddington-DeAngelis functional response and two stage structure on prey, an immature and a mature stage. The time delays are the time lengths between the immature’s birth and maturity prey species. Under some simple assumptions, using upper and lower solutions method and a comparison principle we prove that the unique constant positive steady states solution is global asymptotic stability. The results shows that the dynamic behavior of solutions to this model is similar to that of solutions to corresponding model without diffusion.
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