Analysis Of Dynamic Behaviors For Two Kinds Of Prey-predator Models With Interference

With the development of the science technology, changing every day, in the enjoyment of science and technology, bad consequences of science and technology are infected the biological systems, such as: air pollution, water pollution, food on the decline, the aggravation of interspecific and intraspecific interference, which make the species endangered. In order to keep the diversity of species, this paper adds shelters to the biological mathematical model. At the same time, the pollution factor is widespread in the actual systems, considering the influence of pollution to biological model is necessary. Because pollution cannot immediately affect the biological systems, and it usually has the effect of delay and randomness, using the random delay system to describe the biological model, this paper analyzes the dynamic behavior of two kinds prey-predator models based on the prey-predator model.Firstly, this paper introduces the shelter effect of predator-prey model, the research significance and status of perturbation systems and time-delay systems, and puts forward the research problem studied in this paper. Some knowledge related to this paper is also given.Secondly, we add the shelter to the prey-predator model with interference influence and use the Holing-II response function with the shelter effect and the Jacobin determinant to analyze the stability of the system at the equilibrium point. Next we give the global stability conditions of the shelter effect when system is stable and conditions of limit cycle of the shelter effect when system is unstable. Then according to the parameters of a practical example, we get the matlab simulation picture through a numerical simulation, which proving that the controllers obtained have valid control to the system.At last, we discuss a prey-predator model with pollution and disturbance. Considering the influence of pollution factor to all biological system and randomness of the system, we do linear transformation to the system. Using formula and standard Brownian motion theorem, we analyze the stability of prey-predator system with pollution and disturbance, and get that the persistence of system without pollution, and non-persistence and extinction of the polluted system. Finally, a numerical simulation given proves the rationality of the conclusions obtained in this paper.