Methematical Analyses For Several Discrete Time Population Dynamic Systems

As is well-known to all,studying the discrete time population dynamic models not only has the extensive biological significance,but also has the value of practical application.In recent years, more and more scholars at home and abroad are interested in the studying of the discrete population models and many research results are already obtained.This paper, we wish to continue such studies.We investigate the permanence of a class of discrete predator-prey model with functional responses,the stability of the optimal harvesting of discrete model of a single-species with birth stage-structure and dynamical properties of birth pulse and pulse harvesting effects.Four parts of main work are as followsFirstly, we introduce the biological background and relevant biomathematical background of the discrete time population models.Then some existing research results are given.Secondly, by applying the comparison theorem of difference equation,we study a predator-prey model with monotonic functional responses.Then sufficient conditions for the permanence of the system are obtained.Thirdly,we study the stability of the optimal harvesting of discrete model of a single-species with birth stage-structure.Here by constructing a suitable Liapunov functional,we discuss stability condition for this model and by using theorem on existence and uniqueness of solution, we obtain the optimal harvest effort.Finally,based on previous model,wc study the dynamical properties of birth pulse and pulse harvesting effects by applying pulse principle.And we obtain the existence condition for the optimal harvesting effort.