A Predator-prey Stochastic Model With HollingⅡ Functional Response

The dynamic relationship between predators and their preys always play an importantrole in both ecology and mathematical ecology. Lots of models are studied, including theLotka-Volterra models and more complex Holling type Ⅱ or Holling type Ⅲ functionalmodels.All population systems are often subject to environmental noise, so it is reasonable tointroduce noise into the predator-prey models and yield the stochastic predator-preymodels. Different deterministic population models yield the corresponding stochasticversions when the environmental noises are introduced. In this thesis, by stochasticallyperturbing all parameters in deterministic predator-prey model with Holling Ⅱ type, weconsider the corresponding stochastic predator-prey model with Holling Ⅱ type model.The outline of this paper is as follows:Chapter1introduces the background and the development of the population models.Chapter2gives some elementary symbols, notations and some necessary Lemmas.Chapter3examines the existence-and-uniqueness theorem of the stochasticpredator-prey model with Holling Ⅱ type by using the Lyapunov function, and gives theasymptotic properties of this solutions, including the growth rate, boundedness, stochasticpermanence and moment average in time.Chapter4presents the conditions under which the stochastic predator-prey modelwith Holling Ⅱ type has a stationary distribution and the ergodic property.Chapter5gives the numerical simulation by using the Milstein method and Matlabsoftware.Chapter6shows that some existing stochastic predator-prey models can be seen asthe special cases of the models in this thesis.