Here, the authors investigate the stage-structured autonomous predator-prey Lotka-Volterra system with time delay:
where and represent the densities of mature and immature of predator species, respectively, while and represent the densities of mature and immature of prey species, respectively. denotes the length of time from the birth to maturity of ith species. The basic properties of the model investigated are the boundedness of positive solutions to the system. Further, the authors obtain some conditions for the global asymptotic stability of the unique positive equilibrium point. Moreover, in the system the prey population get extinction and the predator population get permanence are investigated. Finally, the authors present a theorem extending corresponding conditions when there are no two stage structures.