Stability And Bifurcation Analysis For A Modified Leslie-gower Predator-prey Model With Michaelis-menten Type Harvesting In Prey

The investigation of prey-predator systems is not only benefited to the survival and competition among various organisms,but also benefited to the reasonable collocation of living space and conditions of human beings.In order to use effectively ecosystems and can benefit from it,we must study the behavior of prey-predator system in depth.In this paper,a modified Leslie-Gower two-species prey-predator model with Michaelis-Menten type harvesting in prey is considered.This paper is arranged as follows:The first chapter briefly describes the research background,significance and current situation of modified Leslie-Gower two-species prey-predator models with MichaelisMenten type harvesting in prey,and points out the main work to be done in this paper.The second chapter introduces the essential basic knowledge,main definitions and lemmas of the subject.In Chapter 3,we discuss the existence of equilibrium point of the system studied in this paper.Chapter 4 mainly studies the local asymptotic stability and the global asymptotic stability of the interior equilibrium point and the existence of the Hopf bifurcation.The conclusion is verified by proper numerical simulation.Chapter 5 discusses the existence of saddle-node bifurcation and Bogdanov-Takens bifurcation at the coexistence equilibrium point by calculating the normal form of saddlenode bifurcation and Bogdanov-Takens bifurcation.