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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (3): 425-431.doi: 10.3969/j.issn.1005-3085.2015.03.011

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具有单个反馈控制变量的非自治差分两种群竞争系统的持久性和全局吸引性

王丹红   

  1. 闽江学院数学系，福州 350108
  • 收稿日期:2013-11-22 接受日期:2014-05-16 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    福建省自然科学基金 (2012J05007).

Permanence and Global Attractivity of a Nonautonomous Discrete Two Species Competitive System with Single Feedback Control

WANG Dan-hong   

  1. Department of Mathematics, Minjiang University, Fuzhou 350108
  • Received:2013-11-22 Accepted:2014-05-16 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The Natural Science Foundation of Fujian Province (2012J05007).

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摘要： 从环境保护的角度看，持久性和稳定性是生态系统非常重要的性质，而外界因素对生态系统的干扰是不可避免的，所以研究反馈控制下生态系统的稳定性具有较大的理论意义．本文提出一类具有单个反馈控制变量的非自治差分两种群竞争系统，并利用比较原理和微分中值定理，得到了保证系统持久和全局吸引的充分条件．最后，通过数值模拟验证了所得结论的可行性．

关键词: 非自治差分, 反馈控制, 竞争系统, 持久性, 全局吸引性

Abstract:

From the perspective of environmental protection, the permanence and stability are important characteristics of ecosystems. However, it is inevitable that external factors have influence on ecosystems, so it is important for us to study theoretically the stability of an ecosystem under the condition of feedback control. In this paper, we firstly propose a nonautonomous discrete Lotka-Volterra competitive system with a single feedback control. Furthermore, by utilizing the standard comparison theorem and the differential mean value theorem, we obtain the sufficient conditions for the permanence and global attractivity of the system. Finally, a numerical example shows the feasibility of our main results.

Key words: nonautonomous difference, feedback control, competitive system, permanence, global attractivity

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