Dynamics Of IGP Model With Fear Effect And Discrete Time Delay

In biomathematics,the Intraguild Predation(IGP)model,which combines predation and competition,is the focus of many researchers.Based on IGP model,this paper studies the dynamic behavior of IGP model with fear effect and discrete time delay.This dissertation consists of three chapters.In chapter 1,the background of IGP model,the status of IGP model and fear effect are briefly introduced,some basic theorems are given,and the main research work of this paper is summarized.In chapter 2,a class of IGP model with fear effect and discrete time delay is established.Firstly,the well-posedness of the model is proved,and the existence conditions of boundary equilibriums and positive equilibrium are given.Then,the instability of trivial solutions,the globally asymptotic stability of semi-trivial solutions and boundary equilibrium(when there is no IG prey)are studied.Moreover,the local asymptotic stability and Hopf bifurcation of boundary equilibrium(when there is no IG predator)and positive equilibrium are discussed.Finally,combining the formal adjoint theory,the center manifold and the normal form theory,the direction and stability of the Hopf bifurcation generated at the positive equilibrium are analyzed.In chapter 3,the results of stability analysis are verified by numerical simulation,and the influence of fear effect on IGP model is analyzed.The analysis shows that the stability of boundary equilibrium(when there is no IG predator)and positive equilibrium will change with the change of fear coefficient and time delay parameters.In addition,at the boundary equilibrium point(when there is no IG predator),when the fear coefficient is very large,the population density of IG prey will be small and even go extinct.