The Survival Analysis And The Economic Harvesting Policy Of Single-species In A Polluted Environment

This article concentrates on the study of a mathematical model for the effect of toxicant levels and harvest on a single-species ecosystem. The studies of species in polluted environment are mostly based on the model of Hallam and his coworkers~[2,3,4] in which some factors are not considered. B.Buonomo considered the above factors and founded a more reasonable model ~[1] But the effect of harvesting has not been considered in his model. Based on the model in paper [1], we give the improved model of single-species in the polluted environment with the consideration of harvesting.The model is the folowing (Ml).We use the comparison theorem to prove that the system (Ml) have bounded solutions. Applying the boundness and some propertities of the mean of integration, we get the sufficient condition of weak persistence in the mean, and the curve of demarcation between weak persistence in the mean and going-to death. An optima! allocation of efforts towards treating pollution and harvesting population has been obtained in the economic model with the above two factors. We use Pontryagin's maximum principle to solve the optimization problem, and the optimal solution has been gotten which absorbs the suboptimal path.The tree of this paper is as the following. In introduction, we focus on the background of the problem being investigated. In chapter one, we establish the model and do some preparations. In chapter two ,we analyse the survival problem of species. In chapter three, the optimal economic harvesting policy has been obtained with the consideration of treating pollution and harvesting efforts.