环境污染下的具有非线性捕获的捕食食饵系统的稳定性和最优税收  

Optimal Taxation and Stability of a Predator-Prey System Incorporating Nonlinear Harvesting in a Polluted Environment

作　　者：赵亮 陈凤德[3] ZHAO Liang;CHEN Feng-de(School of Mathematics and Information, Fujian Normal University, Fuzhou 350117, China;School of Information and Statistics, Guangxi University of Finance and Economics, Nanning 530003, China;College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350116, China)

机构地区：[1]福建师范大学数学与信息学院,福州350117 [2]广西财经学院信息与统计学院,南宁530003 [3]福州大学数学与计算机科学学院,福州350116

出　　处：《西南师范大学学报（自然科学版）》2020年第9期31-36,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11771082);广西财经学院青年教师科研发展基金项目(2019QNB09).

摘　　要：研究了一类环境污染下的具有非线性捕获的捕食食饵系统的稳定性和最优税收.首先分析了该系统平衡点的存在性,然后通过计算雅克比矩阵的特征值以及构造适当的Lyapunov函数给出了保证系统平衡点的局部稳定性和正平衡点全局稳定的充分性条件,最后利用Pontryagin最大值原理得到了达到最优税收的最优平衡解.A predator-prey system incorporating nonlinear harvesting in a polluted environment has been studied in this paper.Firstly,the existence of equilibrium of the system has been discussed.Secondly,some sufficient conditions for the stability of the system have been obtained by calculating characteristic value of Jacobian matrix and constructing a suitable Lyapunov function.And lastly,the optimal taxation policy is obtained by using the Pontryagin's maximal principle.

关 键 词：捕食食饵 环境污染 非线性捕获 稳定性 最优税收 

分 类 号：O175.14[理学—数学]