The Study Of Stochastic Predator-prey System With White Noise

In this thesis,the effects of the predator-prey system under white noise are studied.We apply the population ecology method and the stochastic differential equations like It? formula,Lyapunov function and Chebyshev inequality.The refuge of prey population,the time delay as well as the stage-structure of species are considered in the analysis process.The contributions of this thesis are as follows:(1)The stochastic predator-prey system incorporating a prey refuge and Holling?functional response is investigated.A unique global positive solution for the stochastic system has been studied.The positive solution is stochastically ultimately bounded.The sufficient conditions of global stochastically asymptotic stability of the positive solution are derived.(2)The stochastic predator-prey system of two preys and one predator with time delay is investigated.The existence of the global positive solution is proved.In addition,the stochastically ultimately bounded of the solution is analyzed.The sufficient conditions of extinction and persistent in the mean of each population are derived by stochastic comparison theorem and It? formula.(3)The predator-prey system incorporating a prey refuge and a stage-structure is investigated.The global asymptotic stability of the positive equilibrium solution is obtained.The stochastic predator-prey system with the random of white noise is discussed at the same time.The existence of the global positive solution and the stochastically ultimately bounded of the solution are derived.We found that the positive equilibrium solution of the system is global stochastically asymptotic stability when the white noise is small enough.By studying of the three types of the stochastic predator-prey system,we found that the white noise has little effect on the global asymptotic stability of the positive equilibrium solution when the white noise is small enough.We also found that the population of the system becomes extinct when the white noise is large enough.The research provides a quantitative guidance to reduce the impact of white noise on the development of population.It also enables the sustainable development of biological populations and human society.