The Dynamical Properties Of Population Model In Protection Zone

Many species are endangered, if we do not act fast, we are going to lose them for-ever. Establishing protection zone is widely used to protect endangered species. Firstly,we study this topic by a new determinate mathematical model. We examine the effectof protection zone and conclude that the protection zone is effective for conservation ofpopulation resources and ecological environment, though in some cases the extinction cannot be eliminated. The dangerous region, the parameters domains and the typical bifur-cation curves of stability of steady states for the considered system are determined. Aswe have all realized, in fact, population dynamics is inevitably affected by environmentalnoise which is an important component in an ecosystem. Taking into account the effectof randomly ?uctuating environment, we incorporate white noise in our model. Then, wegive a stochastic model. How is the effect of this stochastic method? What factors affectthe effect of protection zone? Our results show that the establishment of nature reservescan protect endangered species effectively in good conditions. Under very bad conditions,though protection zone can not protect species from extinction, it also can slow down thespeed of extinction. Based on our results, we give some methods to strengthen the effectof protection zone and provide a method of dividing the protection zone. In addition,we introduce some examples and use several numerical simulations to enhance our mainresults.