Persistence And Periodic Solution Of A Discrete Predator-Prey System With Holling-N Functional Response

In the subject of biomathematic, a predator-prey system with functional response has been the focus of the study. The model of Holling functional response has been recently attracted widely attention in the research of Biological population dynamics.In this paper, we study in the persistence and periodicity of a predator-prey system with Holling functional response. We extend the model with Holling functional response,and discuss the permanence and the existence of periodic solutions for a discrete predator-prey system with Holling-N functional response. The main contents are follows.In the first part, by using the comparison principle and some analytical skills, we obtain a sufficient condition of the persistence of a predator-prey system with Holling-N functional response.In the second part, we study the exsitence of periodic solution for the systems. Firstly, combing Poincarémapping with fixed point theory, we discuss the existence of the periodic solutions. Secondly, by using the theory of coincidence degree, we obtain the sufficient conditions on the existence of the periodic solutions, which are given by means of the mean of periodic coefficients and are more general.