Research On The Permanence Of Four Kinds Of Predator-prey Systems With Stage Structure

In this paper, four kinds of predator-prey ecosystems are studied, sufficientconditions or sufficient and necessary conditions are derived for the permanence ofpredator-prey systems. This paper consists of four parts.Firstly, the permanence of a two-prey one-predator ecosystem with stagestructure is considered. By analyzing the right functions of the ecosystem and usingthe standard comparison theorem, some sufficient conditions are obtained for thepermanence of the ecosystem and non-permanence of predators.Secondly, a stage structured one predator-two competitive prey system withBeddington-DeAngelis (shout for B-D) and Holling Ⅳ functional responses has beenpresented. Based on the comparison theorem, some sufficient conditions are derivedfor permanence of the system and non-permanence of predators.Thirdly, a predator-prey system with stage structured and infinite delay has beenpresented. Making use of the comparison theorem, some sufficient conditions arederived for permanence of the system and non-permanence of predators.Finally, a periodic predator-prey system with Beddington-DeAngelis and Hollingtype functional responses has been presented. By using of the comparison theoremand some results, some sufficient and necessary conditions are derived forpermanence of the periodic system and non-permanence of predators.