Stability Analysis Of Three Classes Of Predator-Prey Systems With Two Impulsive Control

Starting from practical problems of the pest management combining population dynamics with differential equation theory, we discuss the following contents.First, we mainly introduce the research significance and development of predator-prey models. Then we introduce the related basic knowledge and give the research questions in this paper.Second, A Holling type IV Lotka-Volterra one-predator two-prey system with impulsive control on periodic spraying pesticide and releasing enemies at different fixed moment is investigated. By using Floquet theorem and comparison theorem of impulsive differential equation, we prove the pest-extinction periodic solution is globally asymptotically stable. Then the conditions in which the system is permanent are given.Next, based on the biological control strategy for pest management about periodic spraying pesticide and releasing enemies at different fixed moment and considering the resistance of pest, a predator-prey system with impulsive control is investigated. By using Floquet theorem and comparison theorem of impulsive differential equation, we prove the pest-extinction periodic solution is globally asymptotically stable. Then the conditions in which the pest pop are given.Finally, based on the biological control strategy for pest management, a one-predator two-prey delayed model with stage-structured for the prey and impulsive control is considered. By using comparison theorem of impulsive differential equation, sufficient conditions are obtained, which guarantee the global attractivity of pest-extinction periodic solution and permanence of the system.