Qualitative Analysis Of Two Stochastic Population Models

As an important ecological phenomenon,the interaction between predator and prey is a key research topic in population ecology.In recent years,some dynamic properties of population model have been studied extensively by many scholars.At the same time,white noise,Lévy noise and diseases also have important effects on the population ecosystem.Based on the above analysis,this paper mainly studies the effects of white noise and Lévy noise on the three-species food web model and the effects of diseases and white noise on the predator-prey model.The full thesis is divided into four chapters and the structure is as follows.Chapter 1 analyses the research status and significance of population model,and describes the main research contents of this paper.In Chapter 2,the existence and uniqueness of global positive solution for a class of stochastic three-species food web model with Lévy jumps are first given.Then,by constructing appropriate Lyapunov function and applying It? formula and Chebyshev’s inequality,it is found that the model is stochastically ultimately bounded.Moreover,the sufficient conditions of extinction are obtained by using exponential inequality and Borel-Cantelli’s lemma.Finally,some numerical simulations are introduced to illustrate the rationality of the theoretical results.Chapter 3 discusses the existence and uniqueness of global positive solution for a stochastic predator-prey model with disease in prey.Then,by constructing Lyapunov function and applying It^o formula,the strong persistence in the mean of prey population and the non-persistence in the mean of predator population are proved.The extinction of prey population and predator population is obtained by strong law of large numbers.Finally,numerical simulation verifies the rationality of the theoretical results.Finally,the previous work is summarized,and some ideas for further work to be improved are put forward.