Stability Analysis Of Predator-prey System With Bedding-De Angelis And Tanner Functional Response

The survival and development of biotic population are influenced by its living environment. In addition, because of the intervention and the ecological environment pollution caused by human activities, some species even tend to be extinct. Therefore, it has been a hot topic that people are concerned about for a long period of time on how to keep the different organisms thriving under such a condition of limited ecological resources. As Beddington-DeAngelis-type has taken the dual characteristics of both the predator dependent and the prey dependant into account in the description of predator-prey relation, and in order to reveal the relative relationship between predator and prey species more deeply, we must consider many factors which influence the sustainable development of species, such as harvest, investment and pervasion of predator-prey system. So, the prey system under the functional response of Beddington-DeAngelis type is more suitable for the actual ecological system and gets the close attention of many scholars. This paper mainly considers the stability of Beddington-DeAngelis and the system of predator-prey of Tanner and provides theoretical basis for further protection, development and the use of biological resources.The first chapter is the introduction. This part reviews the research background, significance and research status of predator-prey system with Beddington-DeAngelis functional responsereaction, and put forward the main work to be done in this paper.The second chapter is the preliminary knowledge. This chapter mainly introduces the basic concepts and lemmas needed in this paper.The third chapter discusses the prey-predator system model with Beddington-DeAngelis functional response reaction and Tanner reaction. The locally asymptotic stability of equilibria, When the scope of the parameters are different, it will become stable, unstable, or it is possible to appear Hopf bifurcation. The constant conditions and the steady state solution, of locally asymptotic stability are concluded.The fourth chapter discusses the stability of the diffusion of prey-predator system with B-D and Tanner function reaction. while , equilibrium stability is local stabilized. while 1 equilibrium solution is global stabilized.