Research On Two Predator-prey Models With Ratio-dependent Functional Response

In recent years,more and more kinds of species are endagered.Biomathematicians try to use dynamical system method to find the balance which can make the number of species in dynamic equilibrium.Due to discrete dynamical systems with many advantages,this paper explores two discrete predator-prey systems.The first chapter introduces the background,research status and the innovation points.The second chapter introuduces the basic knowledge of the discrete dynamic systems.The third chapter analyses a discrete predator-prey model with Michaelis-Menten functional response.In this chapter,we firstly use the semi-discretization method to transform a continuous system into its corresponding discrete system.Then we use an important lemma to obtain the existence and stability of fixed points.Next we employ the Center Manifold Theorem and bifurcation theory to derive the conditions for the occurrences of flip bifurcation and Neimark-Sacker bifurcation.And we use Matlab software to depict the phase diagram,the bifurcation diagram and the Lynapunov exponent diagram respectively to substantiate all the theorems in this chapter.Finally,we use the EM method and the pseudo maximum likelihood estimation method to estimate parameters.The forth chapter analyses a discrete ratio-dependent Holling-Tanner predator-prey model.Besieds doing the same work in the third chapter,we find the differences between two different discrete methods by comparison.