The Dynamics Properties For Predator-prey Discrete-time Systems With Non-monotonic Functional Response

The predator-prey system dynamics properties have received a great deal of attention of mathematicians and ecologists. To describe the laws of biology, many models described by by continuous or discrete models are built according to the specific circumstances of the population. The models usually reflect the influence of predator-prey relationships of the main factors, such as the density of constraints, functional response and so on. In this paper, we mainly investigate three kinds of nonautonomous predator-prey discrete-time model. We will discuss the persistence, periodicity, almost periodic existence and global attractivity. This paper consists of the following five parts:In the first chapter, we introduce some background and some related researching situations about the predator-prey discrete-time models with nonmonotone functional response. Then, we introduce some predator-prey discrete-time models with nonmonotone functional response which will be studied.In the second chapter, a predator-prey discrete-time model with Holling IV functional response and distributed delays is investigated. By using the comparison theorem of the discerence equation and some analytical technology, some sufficient conditions are obtained for the permanence of the discrete predator-prey system. We discuss the permanent of the system in the following two cases:(a) variable coefficients; (b) periodic coefficients. Also, we present some examples and their corresponding numerical simulations to illustrate the feasibility of the obtained result.In the third chapter, a delayed ratio-dependent predator-prey discrete-time model with nonmonotone functional response is investigated. By using the continuation theorem of Mawhins coincidence degree theory, some new sufficient conditions are obtained for the existence of multiple positive periodic solutions of the discrete model.In the forth chapter, a predator-prey discrete-time model with non-monotone functional response is investigated. By employing the comparison theorem in theory of difference equations, some sufficient conditions are obtained for the permanence of the system under variable coefficients and almost periodic coefficients respectively. At the same time, a set of sufficient conditions about permanent is also set up, which utilizes almost periodic characteristics of system. Furthermore, the criteria which guarantee the existence of a globally attractive positive almost periodic solution of the discrete model is established. An example is given to illustrate the feasibility of the obtained result.At last, the work of this dissertation is concluded. Some problems which were not considered and the direction of research in the future are pointed out in the last chapter.