Qualitative Analysis Of Several Predator-prey Systems And Polynomial System

This paper is divided into two parts. In the first part of the papers, the main research is a few class predator-prey systems, these predator-prey systems are divided into the following several kinds: predator-prey system with crop, predator-prey system with infectious diseases and chain system, but the three kinds of research methods are not equally.First, we studies the N+1type predator-prey system with crop, for this system, we study the stability of equilibrium point, the boundedness, the existence and uniqueness of limit cycle and global stability. and the follow research is the system with N type, a radio-dependent predator-prey model with linear harvesting term and study the limit cycle and equilibrium point.Second, we discuss a predator-infectious disease model, this model use Holling type â…¡ function response function, It is proved that Locally asymptotic stability. Meanwhile, we constructed Lyapunov function to prove the global stability of equilibrium point.Finally, we discussion is a kind of Holling â…¢ type function chain reaction function of predator-prey system, and obtained the persistence and periodic solution and global stability of this model.In the second part of the paper, we discussed the kind of a polynomial system, adopting Dulac method to prove the existence of limit cycle in polynomial system, and the uniqueness of limit cycles by using the generalized Lienard system and numerical simulation. At last, the method to judge the original system and conclusion of, the numerical simulation. The result is also applied to the more general secondary system.