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J4 ›› 2012, Vol. 47 ›› Issue (9): 98-104.

• 数学 • 上一篇    下一篇

一类具有比例和常数脉冲收获的周期竞争系统周期解的存在性

卢拉拉,窦家维   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 收稿日期:2011-05-03 出版日期:2012-09-20 发布日期:2012-09-24
  • 通讯作者: 窦家维(1963- ), 女, 副教授, 博士, 研究方向为脉冲微分方程理论及应用.Email: jiawei@snnu.edu.cn
  • 作者简介:卢拉拉(1987- ),女,硕士研究生,研究方向为脉冲微分方程理论及应用.Email:lula987654@126.com
  • 基金资助:

    国家自然科学基金资助项目(10971124, 61070189)

The periodic solution for a class of competition system with proportional and constant impulse harvesting

LU La-la, DOU Jia-wei   

  1. College of Mathematics and Information Science, Shaanxi Normal University,  Xi’an 710062, Shaanxi, China
  • Received:2011-05-03 Online:2012-09-20 Published:2012-09-24

摘要:

 研究了一类周期环境中既有比例收获又有常量收获的一维脉冲系统正周期解存在的条件以及解的一些基本性质;以此为基础构造一个迭代格式,利用单调迭代方法证明了二维LotkaVolterra竞争系统正周期解的存在定理,得到了保证系统正周期解存在的一组容易验证的充分条件。该方法是构造性的,以利于用数值方法求其周期解。给出一个实例并用数值模拟方法解释说明了所获得的主要结论。

关键词: Lotka-Volterra竞争系统; 比例及常量脉冲收获; 单调迭代方法; 周期解

Abstract:

The existence of the positive periodic solution was studied for a class of periodic logistic equation with impulsive harvesting, which includes both cases of the proportional and constant harvesting. Then, based on the results obtained for logistic equation, a monotone-iterative scheme was established to obtain the existence of the positive periodic solutions for Lotka-Volterra competition system. This method is constructive and can be used to develop a computational algorithm for numerical solutions of the periodic solution. An example was given and some computer simulations were carried out to demonstrate the main results.

Key words: Lotka-Volterra competition system; proportional and constant impulse harvesting; monotone-iterative method; periodic solution

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