文档介绍：具有食饵种群保护的捕食系统的全局稳定性
分析与最优税收策略
刘超1 2,张翼1 2,张庆灵1 2,李元可3
1
东北大学系统科学研究所,沈阳 110819
2
流程工业综合自动化国家重点实验室(东北大学),沈阳 110819
3
东北大学秦皇岛分校数学与统计学院,秦皇岛 066004
摘要:本文建立了具有食饵种群保护的捕食系统,该模型考虑了针对捕食者种群的捕获努力,
同时税收作为调控手段保护捕食者种群免于过度捕获。研究了影响该系统所有正解的有界性条
件。利用微分动力系统理论研究了食饵种群保护水平以及税收的变化对系统所有平衡点的局部
稳定性的影响。进一步,利用 Bendixson 判据研究了系统在正平衡点的全局稳定性。利用
Pontryagin 最大值原理,求出了最优捕获努力量以及与之相关的最优调控税率,保证相关种群
资源的可持续发展与商业捕获的可持续开发。
关键词:运筹学与控制论; 食饵捕食者;捕获努力;食饵保护;最优税收策略; 全局稳定性分析
中图分类号: ;
Global stability analysis and optimal taxation
strategy for a prey-predator system with prey
population refuge
LIU Chao1 2, ZHANG Yi1 2, ZHANG Qingling1 2, LI Yuanke3
1
Institute of System Science, Northeastern University, Shenyang, 110819
2
State Key Laboratory of Integrated Automation of Process Industry, Northeastern
University, Shenyang, 110819
3
School of Mathematics and Statistics, Northeastern University at Qinhuangdao,
Qinhuangdao, 066004
Abstract: In this paper, a prey predator system with prey refuge is proposed, where
selective harvest effort on predator population is considered and taxation is utilized as a
基金项目: National Natural Science Foundation of China, (61104003, 61273008). Research Foundation for Doctor-
al Program of Higher Education of Education Ministry, (201**********). Hebei Province Natural Science Foundation,
(F2011501023). Fundamental Research Funds for the Central Universities of Education Ministry, (N120423009). Research
Foundation for Science and Technology Pillar Program of Northeastern University at Qinhuangdao, (XNK201301).
作者简介: Corresponding author: Liu Chao(1981-),male,associate professor,major research direction:Dynamical
analysis and control of biological system. ******@.. Yi Zhang (1971-), female, associate professor,
major research direction: Dynamical analysis and control of biological system. y.******@. Qin-
ling Zhang (1956-), male, professor, major research direction: Dynamical analysis and control of biological system E-mail: