Analysis Of Predator-prey Model With Spatial Heterogeneity

In recent years,the study of reaction diffusion predator-prey models has been an important topic of ecology and biological mathematics.In the study of predation models,Allee effect and protection zone for the prey has received much attention from many scholars,because they has certain application value in protecting endangered species and maintaining biodiversity,and so on.Based on this,we mainly consider two types of reaction diffusion predator-prey models with Allee effect and a protection zone for the prey in this paper.The main contents are arranged as follows:Firstly,the background and research status of the subject are briefly introduced,two kinds of reaction diffusion predation models with Allee effect and prey protection zone are established,and the main research contents of this paper are listed.Secondly,a reaction diffusion predator-prey model with single Allee effect and prey protection zone is concerned.Applying the method of upper and lower solutions and the comparison principle of parabolic equations,the global existence and dissipation of solutions are showed.The existence and stability of the boundary constant steady state solutions are analyzed,especially the change of stability are pointed out when the predator are a specialist predator and a generalist predator,respectively.By means of Poincare inequality and steady-state bifurcation theory,the existence and nonexistence of the nonconstant steady state solutions of the model are established.Thirdly,a reaction diffusion predator-prey model with double Allee effect and prey protection zone is considered.By using the method similar to the previous chapter,some basic dynamic properties of positive solutions of the model are studied,including the global existence,uniqueness and long time behavior of the solution.The stabilities of the boundary constant steady state solutions are discussed,and the existence and nonexistence of the nonconstant steady-state solutions are proved.In addition,the overexploitation phenomenon is concerned,and the conditions of the occurrence of overexploitation phenomenon are obtained.