Study On The Dynamic Problems Of Two Classes Of Ecological System With Impulsive Control Effect

In this paper, we mainly study on the dynamic problems of two classes of ecological system with impulsive control effect. Several relevant problems attracting more and more attention in this field are deeply discussed.Firstly, the backgrounds and research status on ecosystem dynamic problems are introduced in the essay. It also provides the readers with some preliminaries, including important definitions and lemmas that are frequently used in the following chapters.Secondly, the dynamic problems of a reaction-diffusion ecological system with impulsive control effect have been studied. The threshold conditions for the main dynamic properties are investigated in detail with particular regard to the ultimate boundedness, permanence and extinction. More importantly, the existence, uniqueness and globally asymptotic stability of semi-trivial periodic solution are deeply explored.Furthermore, some correlation dynamics numerical simulations are introduced, which can verify the feasibility and effectiveness of these theoretical derivation theorems, and further reveal the mechanism of impulsive control effect on the dynamical behaviors of the ecological system.Furthermore, the dynamic problems of an ecological system with impulsive control and seasonal effect have been studied. The existence,local asymptotic stability and global asymptotic stability of the semi-trivial periodic solution have been analyzed, and then the extinction and permanence of biological populations have also been discussed.Based on these approaches, we have established the criterion for determining the correlation dynamics properties of the ecological system.All those results can provide some theoretical support for further researching how to utilize impulsive control strategy to maintain the permanence of ecological populations.Finally, the results are summarized and prospected.