On The Dynamical Behaviors In Discrete Lotka-Volterra Competitive System With Feedback Controls

So far, for the discrete-time dynamic model of species persistence, extinction, stability, existence of periodic solutions and so on has been a lot of research results. To examine these dynamics model not only has a wide range of theoretical biology, but also has important practical application value. This paper will discuss the two species competition system with feedback control of discrete-time model of persistent and stability, as well as with a class of discrete-time n-species competition model with feedback control of the extinction. The main contents are summarized as follows:In the first section, we first introduce discrete-time model of species with feedback control biology background. Then introduce a variety of discrete-time model species with feedback control . Finally, we will give in this article research content and organizational structure.Section II, we introduce the persistence of discrete-time two species Lotka-Volterra competition model with feedback control. Is divided into a time-delay and without delay to discuss both cases, using a direct analysis method, direct the right side of the inequality system for zoom, these two types of models have been long-lasting new sufficient condition.Section III, we further discussed the section on the stability of two species model. Here we will take Liapunov function to obtain a sufficient condition for the stability of the system.In section IV, by constructing Liapunov functionals, we study a discrete-time of n-species competition system with feedback control in the extinction . Use this method to obtain discrete-time model for the extinction are more easily satisfied, and There is no question of such research findings.In addition, the application of theorem of this paper give the conclusions of all give the corresponding examples and numerical simulation.