Study On Periodic Solutions And Stability Of Some Kinds Of Ecosystem

This paper includes four chapters.The first chapter is overview. We introduce the state of the study about the predator-prey system of mathematical ecology and our related works.In the second chapter, we consider a kind of Kolmogorov system. The sufficient condition for nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained by using divergence integral, Poincare-Bendixson theorem and Zhang Zhifen'unique theorem.In the third chapter, we are devoted to the qualitative analysis of a class of predator-prey system with Holling III functional response and obtain the sufficient condition for the unique limit cycle of the system. So Yue Zongmin, Hu Zhixing's results are extended.The fourth chapter contains four sections. The first section is preliminary. In the second section, we consider a discrete predator-prey system with delay and general functional response. By using the method of coincidence degree, the sufficient conditions for the existence of at least a periodic solution are obtained. In the third section, a predator-prey system exploited with general functional response is studied. By using similar method, we obtain the sufficient condition for the existence of the periodic solution. In the fourth section, we consider a predator-prey system with impulsive effect and general functional response. The sufficient condition for the existence of the periodic solution is obtained by using similar method.