Study On The Dynamics Of The Stochastic Population Models

In this thesis, a stochastic predator-prey model and a stochasticepidemic model are formulated and analyzed. In this thesis, the papercontains four parts and the main results are as follows:In chapter2, we investigate the complex dynamics of a stochasticpredator-prey model. Some qualitative properties are given. For thestochastic model, we give the existence of global positive solutions,stochastic boundedness, and the global asymptotic stability. Based onthese results, we perform a series of numerical simulations and makea comparative analysis of the stability of the model system withindeterministic and stochastic environments.In chapter3, we study the complex dynamics of a stochasticepidemic model. The sufcient conditions for the stochastic bound-edness, stochastic permanence and stochastic asymptotic stability areobtained. In addition, we perform numerical simulations to validatethe analytical fndings.We note that, when the noise is not large, the stochastic modelpreserves the property of the global stability, that is to say, whenthe noise is not sufciently large, the populations may be stochasticpermanence and stochastic persistent in mean. In this case, we canignore the noise and use the deterministic model to describe the pop-ulation dynamics. But, when the noise is sufciently large, the noisecan force the population to become extinct. In this case, we cannotignore the efect of the noise. That’s to say, in the case of sufcientlylarge noise, we can not use deterministic model but stochastic modelto describe the population dynamics. Our complete analysis of the model will give new suggestions to the studies of the population dy-namics.And in chapter4, we give some discussions and remarks.