The Analysis Of Stochastic Ecological Model With Regime Switching And Time Delay

In this paper, the population ecosystem have been considered, based on the traditional differential model, we add in birth pulse and time delay, and discuss the effect of environmental noise including white noise and colored noise on the traditional ecological system, establish the impulsive and random ecological equation. This paper is arranged as the following chapters:Chapter1give the background and development of population dynamics system and the major work of this paper is introduced.Chapter2a stage-structured predator-prey model with birth pulse and distributed time delay is proposed, conditions for the prey-eradication periodic solution which is globally asymptotically stable and the permanence of the system are obtained, we also use numerical simulation to show the rich dynamic phenomena such as bifurcation and chaos and so on.Chapter3consider the dynamic behavior of a ratio-dependent prey-predator system with random disturbance and Holling II functional response, by applying of Ito’s formula, the Chebyshev inequality and the martingale theory etc, the existence of positive global solutions、stochastically ultimately bounded、stochastic permanence and extinction of the system are obtained, finally, some numerical analysis is given to verify our results, specially the large white noise may bring the extinction of the species.Chapter4is on a delayed random predator-prey system with colored noise, white noise and Markov switching, by virtue of generalized Ito’s formula and ergodicity of Markov, we get the model have a unique positive solution and it is stochastically ultimately bounded. Meanwhile, we get some asymptotic properties, and then we obtain some conditions of species to be extinct.Chapter5summarizes the work of this paper.