Permanence And Periodic Solutions Of The Discrete Population Models

It is well known that studying the discrete time population dynamic models not onlyhas the extensive biological significance, but also with the worth of practical application.In recent years, more and more scholars are interested in the studying of the discretepopulation models, Many research results are obtained. This paper, we wish to continuesuch studies, investigate the permanence of the general nonautonomous discrete timemulti-species Kolmogorov model, and the existence of positive periodic solutions for twodiscrete periodic population models. The main contents can be summarized as follows:In the first section of the first chapter, we introduce the Biological background of thediscrete population dynamic system. In section 2, we introduce the research results fordiscrete time population models. In section 3, the contents and organization in this paperare given.In the second chapter, we mainly analyze the permanence of the general nonau-tonomous discrete time multi-species Kolmogorov model. By using a new method of dis-crete multi-Liapunov functionals, a quite general su?cient condition on the permanenceof the model is established. Applied the general results, new su?cient conditions areobtained to ensure the nonautonomous discrete multi-species Lotka-Volterra competitivemodel with time delays and the food-chain system are permanent, respectively.In the third chapter, by using continuation theorem of coincidence degree theory, theexistence of positive periodic solutions for the following two models are investigated re-spectively: the nonautonomous multi-species periodic Lotka-Volterra discrete competitionmodel with delays and the finite delay discrete predator-prey model with stage structurefor predator. Although the previous one has been studied in some papers, we will givesome better results here. While, for the latter one, there is no investigation.