Analysis Stability Of The Predator-prey System And Hopf Bifurcation

In this paper, a Beddington-De Angelis predator-prey model and a stage-structured predator-prey model with time delay will be considered.The paper is mainly divided into five chapters.The first section is the introduction of the whole paper. We talk about the background of this problem, and make plans for the research of the problems.Next section mainly introduces some elementary knowledge this paper applies.The third section of the paper mainly investigates a Beddington-De Angelis predatorprey modelstudy the equilibria's local and global stability of the system, optimal tax policy is discussed using Pontryagin's maximum principle for conservation of the fishery.The fourth section mainly investigates a stage-structured predator-prey model with time delay,solutions of the system, stability of equilibrium, and the existence, direction, stability, periodic solutions of Hopf bifurcation are discussed.At last, we summarize the results of the whole paper.