中山大学学报自然科学版 ›› 2010, Vol. 49 ›› Issue (3): 12-17.

• 研究论文 • 上一篇    下一篇

非均匀Chemostat竞争模型的周期解

王利娟1,2,姜洪领2   

  1. (1. 陕西师范大学 数学与信息科学学院,陕西 西安 710062;2. 宝鸡文理学院 数学系,陕西 宝鸡 721013)
  • 收稿日期:2009-04-22 修回日期:1900-01-01 出版日期:2010-05-25 发布日期:2010-05-25

Periodic Solution for the Competition Model in the Unstirred Chemostat

WANG Lijuan1,2, JIANG Hongling2
  

  1. (1. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, China;〖JP〗2 Department of Mathematics, Baoji University of Arts and Sciences,Baoji 721013, China)
  • Received:2009-04-22 Revised:1900-01-01 Online:2010-05-25 Published:2010-05-25

摘要: 讨论非均匀Chemostat竞争模型半平凡周期解的存在性、稳定性及其正周期解的存在性。通过运用抛物型方程比较原理、稳定性理论、极值原理以及LeraySchauder度理论,证明了该系统半平凡周期解的存在性和稳定性,得到了该系统正周期解存在的充分条件。

关键词: Chemostat, 稳定性, 度理论, 周期解

Abstract: The existence and stability of semitrivial periodic solutions and the existence of positive periodic solutions for the competition model in an unstirred chemostat are discussed. By using comparison theorems for parabolic equation, stability theory, the maximum principle and the theory of LeraySchauder degree, the existence and stability of semitrivial periodic solutions to the system are proved. The sufficient conditions of existence of positive periodic solutions to the system are obtained.

Key words: Chemostat, stability, theory of degree, periodic solution

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