Dynamic Behavior Of Several Predator-Prey Models

Population model is the most important branch of ecological mathematics, variouspredator-prey models have great ecological meanings. Many authors have paid atten-tion to the study of predator-prey models, and their views are different from each other.By applying the methods of nonlinear analysis, we can obtain the existence of positiveperiodic solutions. By using the knowledge of ordinary differential equations, we canobtain the dynamic properties of models.In this paper, by the results of Mawhin coincidence degree theory, the theory of im-pulsive differential equations and the method of Lyapunov functions in stability theoryof ordinary differential equation, we study the dynamic behavior of several predator-prey models. The paper consists of four chapters.Chapter1introduces the backgrounds and significance of our studies, main workof this paper, preparing knowledge.Chapter2investigates a predator-prey model with Leslie-Gower Holling-type IIand harvesting terms. By means of the generalized Mawhin coincidence degree theory,we show the existence of multiple positive periodic solutions for the system and thepermanence of the predator-prey model.In Chapter3, a neutral delay predator-prey model with Hassel-Varley type func-tional response and impulse is investigated. By using Mawhin coincidence degree the-ory, we obtain some sufficient conditions for the existence of positive periodic solu-tions. We extend some known works in the case of no impulse.Chapter4discusses a predator-prey model with mutual interference and time de-lays. By applying the comparison theorem of the differential equations and constructinga suitable Lyapunov functional, sufficient conditions which guarantee the permanenceand existence of a unique globally attractive positive almost periodic solution of thesystem are obtained. At last, we give examples to illustrate our main result.