The Analysis Of Ecological System With Impulsive Effects And Stochastic Perturbation

In this paper, the ecological dynamics models have been discussed. Based on the traditional differential model, we introduce impulsive effects and stochastic perturbation into traditional differential models. This paper is arranged as follows:Chapter1gives the background of the research and the preliminary knowledge and introduces the main work of this paper.Chapter2is on a delayed stage-structured Watt-type predator-prey model with impulsive effects, conditions for the mature predator-extinction periodic solution of the system which is globally attractive have been established. Also, we get a sufficient condition for the permanence of the system. Besides, numerical simulation is also used to verify the researchChapter3is on a non-autonomous predator-prey system where the prey dispersal in a two-patch environment, with the help of a continuation theorem based on coincidence degree theory, we establish sufficient conditions for the existence of positive periodic solutions. Finally, we give numerical analysis to show the effectiveness of our theoretical results.Chapter4is on a stochastic ratio-dependent predator-prey system with Holling Ⅲ functional response, by the comparison theorem of stochastic equations and Ito's formula, we show that there is a unique positive solution to the system and the positive solution is stochastically ultimately bounded. Moreover, under some conditions, we conclude that the stochastic model is persistent in mean. Besides, a condition for species to be extinct is established. In the end, we use some numerical simulations to confirm our results.