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J4 ›› 2013, Vol. 48 ›› Issue (12): 18-23.

• 论文 • 上一篇    下一篇

一类非自治捕食系统的动力学行为

陈新一   

  1. 西北民族大学中国民族信息技术研究院, 甘肃 兰州 730030
  • 收稿日期:2013-05-31 出版日期:2013-12-20 发布日期:2014-01-09
  • 作者简介:陈新一(1957- ), 男,教授,主要从事微分方程的研究. Email:cxyxbmd@sina.com

Dynamics of the nonautonomous predator system

CHEN Xin-yi   

  1. China Minorities Information Technology Institute, Northwest University for
    Nationalities, Lanzhou 730030, Gansu, China
  • Received:2013-05-31 Online:2013-12-20 Published:2014-01-09

摘要:

研究了一类非自治捕食系统的动力学行为。利用比较原理和构造适当的Lyapunov函数的方法得到了保证此系统持久性和全局渐近稳定性的充分条件,通过Brouwer不动点定理和伴随系统作 Lyapunov函数的方法得到了正周期解和正概周期解的存在性和惟一性。推广了已有的结果。

关键词: 非自治捕食系统; 持久性; 全局渐近稳定性; 周期; 概周期

Abstract:

In this paper, the dynamics of a nonautonomous predator system are investigated. Some sufficient conditions which guarantee the permanence and the global asymptotic stability of the system are determined by using compare theory and constructing a suitable Lyapunov function. For the periodic case and almost periodic case, by using Brouwer fixed point theorems and constructing Lyapunov function to adjoint system, existence and uniqueness of a positive periodic and almost periodic solution are obtained, which generalizes the known result.

Key words: nonautonomous predator system; persistence; global asymptotic stability; periodic; almost periodic

中图分类号: 

  • O175.7
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