Qualitative Analysis Of Two Species Predator Prey System

A kind of food-predator system are considered in this paper. Some background knowledge and the state of study are introduced in the first chapter. Based on the fact, the predator-prey system with functional response are considered, the quality of the equilibrium is discussed, the conditions of the existence and the nonexistence of the limit cycle are provided, and the conclusions of Cheng Rongfu and Yan Tonghua are bettered in the second chapter. The predator-prey system with Beddington-Deangelis functional response and periodic impulsive perturbations on the predator are considered by using the floquet theory of impulsive equation and comparison theorem, sufficient conditions for the system to be extinct and permanence are given in the third chapter. A prey-predator system with sexual favoritism are considered by means of a continuous theorem of coincidence degree theory, a sufficient condition of existence for periodic solution is presented in the fourth chapter. Especially, a sufficient condition of existence for periodic solution for automatic system is given out. The conclusions of Xiuixiang Liu and Youhe Feng are developed.