Study Of The Dynamic Behavior Of Several Predator-prey Systems

This paper mainly studies the dynamics of three types of predator-prey models, the main content is divided into three parts:Firstly, a Holling-Tanner predator-prey model with mutual interference among predators is considered. By comparison theorem of impulsive differential equations, we prove the boundedness of the solution of the system, and discuss the local stability of boundary equilibrium. The conditions of the existence of the positive equilibrium is obtained, further, in these conditions, the local stability and the global stability of the positive equilibrium are obtained. Finally, numerical simulations are carried out to support our results.Secondly, a stochastic predator-prey model with time delay is discussed. By It?o formula, we prove the existence of a global position solution of the considered system and stochastically ultimate boundedness of the solution. Furthermore, the su?cient conditions for persistent in the mean and extinction of each populations are obtained. Finally, numerical simulations are carried out to support our results.Thirdly, a stochastic predator-prey model in a pollute environment is studied. By It?o formula and Chebyshev inequality, we prove the existence of a global position solution of the considered system and stochastically ultimate boundedness of the solution. Then,the su?cient conditions for persistent in the mean and extinction of each populations are obtained. Finally, numerical simulations are carried out to support our results.