The Research On The Existence Of Periodic Solution And The Permanence For A Class Of Discrete Population Models

Based on the existed Lotka-Volterra population models, we consider multi-species models with constant or varied delays instead of two species ones and obtain several classes of discrete delayed population models which seem more practical than those existed. We mainly make much investigation for the existence of periodic solution and the permanence of these new models. This thesis is composed of four chapters.In the first chapter, we state the history of Mathematical ecology's development, the existed related work and the origin of the problems we discussed. And the main work of this paper is also simply introduced.In the second chapter, we consider a periodic Lotka-Volterra cooperative difference system with varied delays. By using the continuation theorem of topology degree theory and properties of nonsingular M-matrix, we obtain sufficient conditions for the existence of positive periodic solutions of this system. As the special case, the results for the two species model are obtained, which are same to the known results of the corresponding differential system.The purpose of the third chapter is to study the permanence of a nonau-tonomous n-species Lotka-Volterra competitive discrete system with delays. By constructing a new qusi-Liapunov function, we obtain some new criteria which are easily checked. The known results of several two-species competitive models are well generalized. On the other hand, although some models cover this model, the required conditions are too rigorous to fit, and the conditions are weakened in our theorems. In this sense, we improve these results.Finally, in the fourth chapter, we still consider a n-species Lotka-Volterra competitive difference system, but this model is a periodic system with different varied delays. The existence of positive periodic solutions of this system is established by using coincidence degree theory.