Impulsive Stochastic Predator-prey Model And Infected Predator-prey Model Subject To Lévy Jumps

This dissertation investigates two impulsive stochastic models in polluted environment with Levy jumps, and one is non-autonomous stochastic predator-prey model, the other is infected predator-prey model.By using the theoretical knowledge of stochastic differential equation,this paper discusses dynamic behavior of these models. First, we show that each models has a unique global positive solution for any given initial positive value. And we obtain conditions for extinction and permanence of the models. This paper includes four sections.In first section, we introduce some background knowledge of the models and conceptions, definitions and theorems of stochastic differential equation.In second section, we study a non-autonomous impulsive stochastic predator-prey model subject to Levy jumps in polluted environment, and we assume that the predator is omnivorous in the model. First, we show that the model has a unique global positive solution for any given initial positive value. Second, the extinction of the population under some appropriate conditions is explored by using Ito formulas. In addition, we obtain the sufficient conditions for the almost sure permanence in mean and stochastic permanence of the system by using the theory of impulsive stochastic differential equations. Finally, simulations are also carried out to illustrate our theoretical analysis conclusions.In third section, we consider the influence of diseases of population,so we explore an impulsive stochastic infected predator-prey model with Levy jumps and delays. First, we build an auxiliary model, and obtain some conclusions of this auxiliary system by using the basic theory of stochastic differential equation. Then in view of comparison theorem, we derive the conditions for extinction. And we obtain the conditions for permanence in the main of stochastic model by using Ito formulas.Finally, we carry out some simulations to verify our main results.In fourth section, we give a summary and prospects. This part summarizes the main results of this paper and explains the biological implications, and then we show the prospects.