基于生态环境和反馈控制的多种群竞争系统的正周期解

数学物理学报 ›› 2017, Vol. 37 ›› Issue (3): 553-561.

基于生态环境和反馈控制的多种群竞争系统的正周期解

傅金波¹, 陈兰荪²

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 10080

收稿日期:2016-09-20 修回日期:2017-03-11 出版日期:2017-06-26 发布日期:2017-06-26
作者简介:傅金波,E-mail:fujinbomnkjxy@sina.com
基金资助:
国家自然科学基金（11371306）和福建省教育厅自然科学基金（JA13370，JAT160676）

Positive Periodic Solution of Multiple Species Comptition System with Ecological Environment and Feedback Controls

Fu Jinbo¹, Chen Lansun²

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

Received:2016-09-20 Revised:2017-03-11 Online:2017-06-26 Published:2017-06-26
Supported by:
Supported by the NSFC (11371306) and the Natural Science Foundation of Fujian Education Department (JA13370, JAT160676)

摘要/Abstract

摘要： 根据种群动力学原理建立了基于生态环境和反馈控制的时滞非自治Lotka-Volterra多种群竞争系统，并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，给出了该系统的正周期解存在性的充分条件.利用Barbalat引理以及构造适当的Lyapunov函数，获得了该系统的正周期解存在唯一性与全局吸引性的代数判据.

关键词: 反馈控制系统, 重合度理论, 全局吸引性, 正周期解

Abstract: In this paper, by using species dynamic theory, a delay nonautonomous LotkaVolterra multiple species competition system with ecological environment and feedback controls is established, and the high order nonlinear function is used in the construction of the feedback control variables. By using Continuation Theorem based on Gaines and Mawhin's coincidence degree theory, the sufficient conditions for existence of positive periodic solution of the system are obtained. Using Barbalat Lemma and constructing an appropriate Lyapunov function, the algebraic criterion for the uniqueness and global attractivity of positive periodic solutions of the system are obtained.

Key words: Feedback controls system, Coincidence degree theory, Global attractivity, Positive periodic solution

中图分类号:

O175.12

傅金波, 陈兰荪. 基于生态环境和反馈控制的多种群竞争系统的正周期解[J]. 数学物理学报, 2017, 37(3): 553-561.

Fu Jinbo, Chen Lansun. Positive Periodic Solution of Multiple Species Comptition System with Ecological Environment and Feedback Controls[J]. Acta mathematica scientia,Series A, 2017, 37(3): 553-561.

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