具有毒物影响和反馈控制的非自治竞争 系统的全局吸引性

doi:10.3969/j.issn.0253-2778.2016.08.003

中国科学技术大学学报 ›› 2016, Vol. 46 ›› Issue (8): 636-641.DOI: 10.3969/j.issn.0253-2778.2016.08.003

• 论著 • 上一篇

具有毒物影响和反馈控制的非自治竞争系统的全局吸引性

傅金波，陈兰荪，程荣福

1. 福建师范大学闽南科技学院, 福建泉州 362332； 2. 中国科学院数学与系统科学研究院数学研究所，北京 100080

收稿日期:2015-10-15 修回日期:2016-05-28 接受日期:2016-05-28 出版日期:2016-05-28 发布日期:2016-05-28
通讯作者: 傅金波
作者简介:傅金波(通讯作者),男，1978年生，硕士/副教授. 研究方向:生物数学. E-mail: fujinbomnkjxy@sina.com
基金资助:
国家自然科学基金（11371306），福建省教育厅自然科学基金（JA13370，JAT160676），福建师范大学闽南科技学院青年骨干教师重点培养对象项目（mkq201006）资助.

Global attractivity of multiple species competition Lotka-Volterra system with toxicants effect and feedback controls

FU Jinbo, CHEN Lansun, CHENG Rongfu

1.Minnan Science and Technology Institute, Fujian Normal University, Quanzhou 362332, China； 2.Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China

Received:2015-10-15 Revised:2016-05-28 Accepted:2016-05-28 Online:2016-05-28 Published:2016-05-28

摘要/Abstract

摘要： 根据种群动力学原理建立了具有毒物影响和反馈控制的非自治多种群竞争Lotka-Volterra系统，在反馈控制变量的构造上采用了高次非线性函数形式.利用重合度理论中Gaines和Mawhin延拓定理，Barbalat引理以及构造适当的Lyapunov函数，获得了该系统正周期解的存在唯一性和全局吸引性的充分条件.

关键词: Lotka-Volterra系统, 重合度理论, 正周期解, 全局吸引性

Abstract: By means of species dynamic theory, a nonautonomous Lotka-Volterra multiple species competition system with toxicants effect and feedback controls was established, and the high order nonlinear function was used in the construction of the feedback control variables. By means of Continuation Theorem based on Gaines and Mawhin coincidence degree theory, Barbalat Lemma and constructing an appropriate Lyapunov function, the sufficient conditions for the uniqueness and global attractivity of positive periodic solutions of the system were obtained.

Key words: Lotka-Volterra system, coincidence degree theory, positive periodic solution, global attractivity

中图分类号:

O175.1

傅金波，陈兰荪，程荣福. 具有毒物影响和反馈控制的非自治竞争系统的全局吸引性[J]. 中国科学技术大学学报, 2016, 46(8): 636-641.

FU Jinbo, CHEN Lansun, CHENG Rongfu. Global attractivity of multiple species competition Lotka-Volterra system with toxicants effect and feedback controls[J]. Journal of University of Science and Technology of China, 2016, 46(8): 636-641.

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具有毒物影响和反馈控制的非自治竞争系统的全局吸引性

Global attractivity of multiple species competition Lotka-Volterra system with toxicants effect and feedback controls

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具有毒物影响和反馈控制的非自治竞争 系统的全局吸引性

Global attractivity of multiple species competition Lotka-Volterra system with toxicants effect and feedback controls

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具有毒物影响和反馈控制的非自治竞争系统的全局吸引性