Dynamics Of A Predator-prey Model With A Double Allee Effect

By means of the theory of nonlinear partial differential equations and bifur-cation analysis,we studied the dynamics of a diffusive predator-prey model with double Allee effect:The main contents are organized as follows:Firstly,we introduce the background and research results of predator-prey mod-els and Allee effect,and give the main results of this thesis.Secondly,we prove the existence and uniqueness of solutions for parabolic e-quations by means of upper and lower solutions method,and give a priori bound of solution.Thirdly,we study the stability of constant steady state solutions for strong Allee effect and weak Allee effect,and discuss the nonexistence of nonconstant positive steady state solutions.Fourthly,we consider the bifurcation direction and stability of the bifurcating periodic solutions for strong Allee effect and weak Allee effect under the case of one-dimensional spatial domain by the center mainfold theory and the bifurcation theory.Finally,we prove the steady-state bifurcation from the simple eigenvalue by means of the Crandall-Rabinowitz bifurcation theory,some numerical simulations are shown to verify the analytical results.