The Research Of Dynamics Character Of Several Kinds Of Discrete Population System

Predator-prey model is a mathematical model which describes the dynamic change in predator-prey system. Since the last century, Volterra and Lotka construct a predator--prey model, predator--prey model has been concerned of many scholars. Most of the scholars are improved on the original model to more appropriate to the actual, They considered the time delay, the functional response, diffusion and many other factors, and to the system stability, permanence and existence of positive periodic solutions of dynamical properties were Rigorous discussion, got a large number of good results. But most of the researches are about continuous model, discrete model and the corresponding research is not very much. In reality, some of the growth process, from generation to generation do not overlap population, establish the discrete model to describe their dynamics can be more effective. This paper discusses some dynamics behaviors of several kinds of discrete models.In the second chapter, based on the continuous model, set up one class with Beddington-DeAngelis functional response predator-prey system, analyzes the model’s persistence, use the theory of topological degree to discuss the Existence of periodic solutions of the condition, And get the discrete predator is a sufficient condition of the global stability of a predator-prey model of the solution.In the third chapter, based on the continuous system with time-delay, plaque, one plaque population dynamical systems with three species were obtained by discrimination. Then analysis the permanence, the existence of periodic solutions,and the global stability of the solution of this system.