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We consider a predator-prey system with Beddington-DeAngelis functionalresponse and delays, in which not only the stage structure on prey but also thedelay due to digestion is considered. First, we give a sufficient and necessary conditionfor the existence of a unique positive equilibrium by analyzing the correspondinglocations of a hyperbolic curve and a line. Then, by constructing an appropriate Lyapunovfunction, we prove that the positive equilibrium is locally asymptotically stableunder a sufficient condition. Finally, by using comparison theorem and the ω-limit settheory, we study the global asymptotic stability of the boundary equilibrium and thepositive equilibrium, respectively. Also, we obtain a sufficient condition to assure theglobal asymptotic stability

Dynamics of a Predator-Prey System with Beddington-DeAngelis Functional Response and Delays