Qualitative Analysis On Two Classes Of Predator-prey Systems With Functional Response

The predator-prey model, since the pioneering work of Lotka and Volterra on it, has received a great deal of attention from many scholars. In this thesis, using the qualitative theory of differential equation, we study two classes of predator-prey systems with functional response. It is composed of three chapters.In the first chapter, some background knowledge, the research significance and the present progress of predator-prey system with functional response are introduced. At the same time, the main work of this paper and some basic theory are presented.In the second chapter, the qualitative behavior of the predator-prey system with functional response is considered, as well as the quality of the equilibrium point is discussed in detail. Besides, the sufficient conditions of existence and nonexistence of limit cycle are obtained from using some theory such as Lienard Transformation, Poincare-Bendixson Theorem.In the third chapter, a class of exploited predator-prey system with nonlinear density condition on prey and non-constant harvesting and Holling-IV functional response on both is investigated. In addition to the study of existence and quality of the equilibrium point, the quality of the infinity is discussed. Moreover, by using Poincare formal series method, the focal values are calculated, hence the stability conditions of the equilibrium point and the nonexistence and existence conditions of limit cycle are obtained.