具有毒素的两竞争鱼群的最优税收问题  

Regulation of Taxation of Two Competing Fish Shoals in the Presence of Toxicity

作　　者：杨海霞 吴应琴 YANG Hai-xia;WU Ying-qin(School of Education,Lanzhou University of Arts and Science,Lanzhou 730010,China;Key Laboratory of Petroleum Resource Research,Northwest Institute of Eco-Environmentand Resources,Chinese Academy of Sciences,Lanzhou 730010,China)

机构地区：[1]兰州文理学院教育学院,甘肃兰州730010 [2]中国科学院西北生态环境资源研究院,中国科学院油气资源研究重点实验室,甘肃兰州730000

出　　处：《兰州文理学院学报（自然科学版）》2021年第1期1-6,共6页Journal of Lanzhou University of Arts and Science(Natural Sciences)

基　　金：国家自然科学基金项目(41772147);兰州文理学院教育教学改革项目“基于数学建模思想下教学模式的改革研究——数学建模思想应用在种群生态学方面的能力研究”;兰州文理学院“线上教学”教改专项立项建设项目(20200124)。

摘　　要：讨论了两竞争鱼群的动态反应模型,每个鱼群都遵守logistic增长规律且为了享用一个共同的食物资源而彼此向对方释放一种毒素物质.为了保护鱼群的过度开发,把税收作为控制工具.验证了系统正平衡点的存在性,讨论了正平衡点的局部稳定性和全局稳定性.最后,利用Pantryagin最大值原理找到了最优税收策略,为生物资源的实际开发与管理提供了必要的理论依据.The dynamic response model of two competing shoals was discussed.Each shoal obeyed logistic growth rule and released a toxin to each other in order to enjoy a common food resource.To protect the overexploitation of fish stocks,taxation was used as a control tool.The existence of the positive equilibrium point was verified,and the local stability and global stability of the positive equilibrium point were discussed.Finally,the Pantryagin maximum principle was used to find the optimal tax strategy,which provided the necessary theoretical basis for the actual development and management of biological resources.

关 键 词：动态反应模型 竞争 毒素 税收 最优收获策略 

分 类 号：O175[理学—基础数学]