Existence Of Equilibriums And Periodic Solutions For Predator-prey With Predator Harvesting And Prey Refuge

In this paper,we consider a class of predator-prey model with Holling type II functional response and constant-rate predator harvesting incorporating a constant prey refuge,and extend the corresponding results in the model.In Chapter 1, we introduce the research results of both at home and abroad about prey-predator model, and put forward the new predator-prey model:In Chapter 2, we consider the existence of positive equilibriums of this class of predator-prey model with Holling type II functional response and constant-rate predator harvesting incorporating a constant prey refuge, and obtain necessary and sufficient conditions for ex-istence of unique positive equilibrium or two positive equilibriums. What’s more, the locally quality of the equilibrium is analyzed by using the method of characteristic root.Finally, the results are obtained respectively which are similar with the corresponding those on [Dong-mei Xiao, Wenxia Li, Maoan Han, Dynamics in a ratio-dependent predator-prey model with predator harvesting[M], J Math Anal Appl,2006,324:14-29] and [Lili Ji, Chengqiang Wu, Qulitative analysis of a predator-prey model with constant-rate prey harvesting incor-porating a constant prey refuge[M], Nonlinear Analysis:Real World Applications,2010,11: 2285-2295].In Chapter 3, we change the positive constants into the positive w-periodic functions. By utilizing the coincidence degree theorem, some sufficient conditions for existence of positive periodic solutions are obtained respectively which are similar with the corresponding those on [Xinrnin Wu,Jingwen Li,Zhicheng Wang, Existence of positive periodic solutions for a generalized prey-predator model with harvesting term, Computers and Mathematics with Application 55(2008)1895-1905].