A Type Of Qualitative Analysis With A Fear Effect Model

In the thesis,by using the theory and method of the partial differential e-quations and nonlinear analysis,the steady state positive solution of predator-prey model with fear effect under different boundary condition is studied.Firstly,we discuss predator-prey model with fear effect under homogeneous Dirichlet boundary condition by using the maximum principle and bifurcation the-ory.The model is as follows:Secondly,we discuss predator-prey model with fear effect under homogeneous Neu-mann boundary condition by using the linear stable theory and degree arguement.The model is as follows:The main contents in the thesis are as follows:In chapter 1,the development and research significance of predator-prey mod-el are summarized,and the research background and practical significance of the predator-prey model with fear effect are proposed.In chapter 2,the bifurcation and stability of the positive solutions of the predator-prey model with the fear effect under the homogeneous Dirichlet boundary condition are studied.First of all,a priori estimate of the positive solution is given by the comparison principle.Secondly,through the local bifurcation theory,we treat m as bifurcation parameter and discuss bifurcation phenomenon of a semi-trivial solution(m*;?,0)in this system.In addition,by combining the global bifurcation theory,we extend the solution from local bifurcation to global bifurcation,and give the trend of the global bifurcation solution.Finally,the stability theory of the bifur-cation solution is used to show the stability of the solution,and the local bifurcation solution is unconditionally stable.In chapter 3,the existence of positive solution of predator-prey system with fear effect under homogeneous Neumann boundary is studied Firstly,a prior esti-mate of solution is obtained by using the maximum principle.Secondly,by applying the linear stability theory,the stability of the positive solution of steady-state is ob-tained.Finally,the existence of positive solutions is got by using the Leray-Schauder theory.