The Study Of Some Classes Of Predator-prey Models With Impulsive

In this paper, we mainly study the dynamics of some classes of predator-prey model with impulsive. The article includes four chapters.The preface is in chapter 1. we introduce the research background of this article, the main task and some important preliminaries.In Chapter 2, we propose a delayed predator-prey model with birth pulse and impulsive harvesting in a polluted environment. Existence conditions of the predator-extinction periodic solution are derived by developing the stroboscopic map. Further, we discuss the global attrac-tivity of predator-extinction periodic solution and permanence of the system, and obtain the threshold conditions. The results provide a dependable theoretical strategies to protect popula-tion from extinction in a polluted environment. Finally, the numerical simulations are presented for verifying the theoretical conclusions.In Chapter 3, we propose a single species model with impulsive diffusion and pulsed har-vesting. Using the discrete dynamical system determined by the stroboscopic map. we obtain a positive fixed point and show that the positive fixed point is globally stable when harvesting for the population is less than certain value or when the period of pulsing over certain value. Correspondingly, the single species system with impulsive diffusion and pulsed harvesting always has a globally stable positive periodic solution. The main theoretical results are illustrated with numerical simulations.In Chapter 4, we propose a predator-prey model with epidemic in the predator containing B-D functional response function. The model considers a constant ratio prey refuge. Depending on a constant ratio prey refuge n, which provides a condition for protecting prey from predation, we show the existence and stability properties of the equilibria for the model. Furthermore, the sufficient condition for system persistence is obtained through standard comparison theorem. Finally, the numerical simulations are presented for the accuracy of theoretical results..