Dynamic Analysis About A Diffusive Predator-prey Model With Allee Effect And Multiple Delays

Population ecology is a branch of science that studies the dynamic changes of the species in order to forecast the future development of species.And then some corresponding measures are taken according to it.Predation is an universal phenomenon in nature.The study of the predation system provides some theoretical guidance for the sustainable development and manegement of the biogogical population.In this thesis,we consider a diffusive predator-prey model with Allee effect and multiple delays.The details are organized as follows:The first chapter is the introduction about the background and significance of the selected topic,including the research status and the main works of the thesis.We mainly discuss the existence and local stability of the equilibrium points for the system without time delay in the second chapter.In the third chapter,the boundedness of the solution and persistence for the system are proved by using comparison theorem.In addition,based on the qualitative and stability theory of differential equations and Hopf bifurcation theory,the local stability of the equilibrium and the existence of Hopf bifurcation are demonstrated under time delays.Futhermore,the sufficient conditions for global stability of the positive equilibrium are obtained by constructing a suitable Lyapunov functional.Some numerical simulations have been carried out in order to illustrate our theoretical analysis.The last chapter is a summary of this thesis and comments on the prospect study for the future research.