Dynamics Analysis Of Tow Types Of Stochastic Predator-prey System

With the rapid development of population ecology,it was found that compared with the traditional differential and difference system,stochastic differential system can more accurately describe the population dynamical system.In this thesis,some theories related to stochastic dynamics system and stochastic differential equation are used to investigate dynamical behaviors of stochastic predator-prey system under environmental noise and time delay.The research contents are as following:Firstly,a Crowley-Martin type prey-predator system with delay and white noise is discussed.By constructing the appropriate Lyapunov function,use of It? formula and some of the inequality technique,proved the property of global positive solution(existence,uniqueness and asymptotic pathwise estimation),the sufficient conditions of stochastically persistence and global stochastic asymptotic stability are obtained.Finally,some simulation figures are shown to verify the validity of our results.Secondly,the effect of white noise and L?vy noise in the growth rates is considered and the corresponding stochastic predator-prey system is established.By constructing the appropriate Lyapunov function and using It? formula and some of the inequality technique,the property(existence,uniqueness and stochastically ultimate boundedness)of the positive solution of the system is proven.The sufficient conditions that guarantee the permanence,extinction,stationary distribution and ergodicity of the system are achieved.Finally,numerical simulation are conducted to verify the effectiveness and feasibility of the obtained results.