The Research Of Dynamics Character Of Two Classes Of Discrete Predator-Prey System

Predator-prey model is a mathematical model which describes the dynamic change in predator-prey system. In 1921 and 1923, Lotka and Voterra came out with Lotka-Volterra system respectively. This model aroused people's wide concern. Many research men considered some important factors like stage structure, time delay, parental care and so on, and work out a lot of important conclusions which made a great step forward in the model. In real life, we need to use the discrete models to study non-overlapping generations population. In this paper, we will discuss the dynamical behaviors of the discrete models.In chapter 2, we firstly introduce some related the knowledge which will be applied, including the mapping of the type of bifurcation, bifurcation theories, the condition of Jury and the center manifold theorem.In chapter 3, according to the continuous model,a discrete predator-prey model with harvest is established, which considering different capture object and capture strategy models, the existence of the equilibriaare are analyzed, local asymptotic stability of the equilibria are argued by Jury's condition, condition of bifurcation are also obtained by useing center manifold theorem and bifurcation theories.In chapter 4, according to the continuous model,a discrete predator-prey model with delay and harvest is established,the existence of the equilibria which without delay and delay models are analyzed, local asymptotic stability of the equilibria are argued by Jury's condition.