The Study Of Dynamic Properties On A Stochastic Population System

In this thesis, some theories related to stochastic dynamics system and stochastic differential equation, constructing the appropriate Lyapunov function and some of the inequality technique are used to investigate dynamical behaviors such as the property of global positive solution(existence, uniqueness and stochastically bounded), permanence, extinction and global asymptotic stability. The following results are obtained:At first, based on a predator-prey model with Beddington-De Angelis functional response which the scholar only took into account the white noise and the coupled mode of the two noise sources is very simple, one noise source has an effect on both predator and prey is considered. By constructing the appropriate Lyapunov function, ?Ito formula and some of the inequality technique, the property of global positive solution and sufficient conditions which guarantee the stochastically permanence and extinction of the stochastic system are obtained. Furthermore, some simulation figures are shown to verify the validity of our results.Then, based on a predator-prey model with Crowley-Martin functional response and considering the effect of white noise in the growth rates, a corresponding stochastic dynamics model is established. Using ?Ito formula and some of the inequality technique repeatedly and constructing the appropriate Lyapunov function, sufficient conditions for the stochastically permanence, extinction and global asymptotic stability of system are given, respectively. At last, some simulation figures are shown to verify the validity of our results.At last, based on the above considering the effect of white noise in the growth rates, we further take into account the effect of white noise and color noise(which can modelled by Markov chains) in the growth rates. A predator-prey model with Holling II functional response is established and the property of global positive solution such as existence, uniqueness, stochastically bounded is studied. By using ?Ito formula and some of the inequality technique repeatedly and constructing the appropriate Lyapunov function, the sufficient conditions for global asymptotic stability are also established. Besides, some simulation figures are shown to verify the validity of our results.