一类食饵—捕食征税模型分析  

Analysis of a Prey-predator Model with Taxation

作　　者：孙军芳[1] 张睿[1] 陈红兵[2] 

机构地区：[1]兰州交通大学数理与软件工程学院,甘肃兰州730070 [2]天水师范学院数理与信息科学学院,甘肃天水741001

出　　处：《佳木斯大学学报（自然科学版）》2007年第5期654-656,共3页Journal of Jiamusi University：Natural Science Edition

基　　金：中国博士后科学基金资助项目(20060390028)

摘　　要：在两种群相互作用的Logistic模型的基础上将税收考虑进去分析了一类食饵—捕食收获模型.讨论了正平衡点的存在性,证明了正平衡点的局部渐近稳定性,利用Pontryagin最大值原则得到了最优税收策略.In this paper, a prey - predator system based on Logistic model with selective harvesting and taxation is considered. The existence of positive equilibrium of the system is discussed. The local stability analysis has been carried out. An optimal tax policy is given using Pontryagin＇ s maximum principle. The objective is to maximize the monetary social benefit as well as conservation of the ecosystem.

关 键 词：食饵—捕食 平衡点 渐近稳定 最优税收 

分 类 号：O175.1[理学—数学]