Research On A Predator-prey Model With The Fear Effect And Intraspecific Competition

Based on the predator-prey model with Holling type ?functional response,we consider the effect of fear effect on the population dynamics of predator-prey model.In Chapter 2,we establish a predator-prey model with fear effect and intraspecies competition of prey.It is further considered that due to natural reasons such as the shortage of survival resources,prey populations migrate between different patches in order to obtain enough food resources.Therefore,a predator-prey model with fear effect and prey migration between two patches was established in Chapter 3.For a predator-prey model with fear effect and intraspecies competition,we first prove the positive and uniformly boundedness of the solution under initial conditions.Then,the relative properties of equilibrium points of the model are analyzed,and the conditions of existence of each equilibrium point,local asymptotic stability and global asymptotic stability of coexistence equilibrium point are obtained.Furthermore,the uniform persistence condition of the model and the existence condition of Hopf burfications are analyzed.Finally,the theoretical analysis results were numerically simulated by MATLAB,and the influence of fear effect on the existence of coexistence equilibrium point and population density of each population was analyzed.For the predator-prey model with fear effect and prey migrating between two patches,we first prove the positive solution of the model,and analyze the stability of the model equilibrium point under two conditions: no prey migration and migration.Then,the conditions for the existence of equilibrium points,the local asymptotic stability,the uniform persistence of the model and the existence of Hopf burfications are obtained through theoretical analysis.Finally,the results of theoretical analysis are verified by numerical simulation,and the effect of mobility on the dynamic behavior of the model is discussed.