The Dynamical Properties On Some Ecosystems

This paper includes five chapters.The first chapter is overview. We introduce the state of the art about the population dynamics of mathematical ecology and our related works.In the second chapter, we consider a kind of Kolmogorov system. The sufficient conditions of nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained. So the results of Yan Xiangping, Zhang Cunhua etc are extended.In the third chapter, we study a predator-prey system with functional response, which the prey species are stocked. When the prey species are controlled in ration, we obtain the necessary and sufficient condition for the unique limit cycle of the system. So Chen Liujuan and Sun Jianhua' s results are extended.The fourth chapter contains four sections. The first section is preliminary. In the second section, we consider a predator-prey system with Beddington-DeAnge-lis functional response, which the prey species satisfy nonlinear growth. The sufficient conditions for the persistence and the existence and uniqueness of periodic solution are obtained. So our results extend Fan Meng and Kuang Yang' s some results. In the third section, a delayed predator-prey system with general functional response are studied, which the prey species also satisfy nonlinear growth. And we obtain the sufficient condition for the existence of the periodic solution. So Wang Linlin and Li Wantong' s result about the existence of periodic solution is extended. In the fourth section, we consider a delayed predator-prey system with more general functional response. The sufficient condition for the existence of the periodic solution is obtained. And our result extend Ye Dan, Fan Meng and Zhang Weipeng' s result.In the fifth chapter, we consider a nonlinear asymptotically multispecies competition predator-prey system with general functional response. The...