Dynamical Behaviors Of Stochastic Ecosystem With Impulsive Effects And Time Delayed

This paper focuses on the study of three population ecology models: astochastic predator-prey model with Beddington-DeAngelis type function response,a stochastic predator-prey model with impulsive effects and a stochasticpredator-prey model with time delaye.Chapter1begins with introduction of the research background and primaryworks which have been done in this paper.Chapter2consider a stochastic predator-prey model with Beddington-DeAngelis type function response. In this model,we taking several randomperturbation factors into consideration, utilizes Ito ’s formula, the Chebyshevinequality to reach the conclusions of the existence of systematic solution, stochasticpermanent, stochastically ultimately bounded and extinction of the model.Chapter3study a stochastic non-autonomous predator-prey system withimpulsive effects and Beddington-DeAngelis type function response. By usingIto ’s formula, inequality of the differential equations, comparison theory and theequivalent relation between the solution of non-autonomous stochastic differentialsystem with impulsive effects and that of a correspongding non autonomousstochastic differential system with impulsive effects, we conclude the stochasticmodel have a unique positive global solution and boundedness, uniformly boundedin the mean and the condition of extinction.Chapter4discuss a stochastic predator-prey model with time delayed. Weanalysis a improved delay model have positive equilibrium and its Hopf bifurcationwithout white noise. By perturbing growth rate of prey population and death rate ofpredator population, with noise terms,we construct the stochastic delay differentialsystem. By using Ito ’s formula and stochastic comparison theory, we show thatthe system admits unique positive solution and tochastically ultimately bounded.Chapter5summarizes the work of this paper.