Coexistence states of unstirred Chemostat model with C-M functional response

Computer Engineering and Applications ›› 2014, Vol. 50 ›› Issue (7): 30-34.

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Coexistence states of unstirred Chemostat model with C-M functional response

JIANG Hongling1，2，LI Haixia1，2

1.College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
2.Department of Mathematics, Baoji University of Arts and Sciences, Baoji, Shaanxi 721013, China

Online:2014-04-01 Published:2014-04-25

带C-M反应项的非均匀恒化器模型的共存态

姜洪领1，2，李海侠1，2

1.陕西师范大学数学与信息科学学院，西安 710062
2.宝鸡文理学院数学系，陕西宝鸡 721013

Abstract

Abstract: The existence and stability of the positive solutions for an unstirred Chemostat model with Crowley-Martin functional response are considered. Firstly, by means of the fixed point index theory, the sufficient conditions for the existence of the positive solutions are determined. Moreover, the stability of the local positive solutions is investigated by using the perturbation theorem for linear operators and the stability theorem for bifurcation solutions. The results indicate that the two species will coexist under certain conditions, furthermore the coexistence solutions are stable.

Key words: Chemostat model, Crowley-Martin functional response, fixed point index, stability

摘要： 讨论了一类带有Crowley-Martin反应项的非均匀Chemostat模型正解的存在性和稳定性。运用不动点指数理论得到了正解存在的充分条件；利用线性算子的扰动理论和分歧解的稳定性理论讨论了局部正解的稳定性。结果表明在一定条件下，两物种能共存，而且共存解稳定。

关键词: Chemostat模型, Crowley-Martin反应函数, 不动点指数, 稳定性

JIANG Hongling1，2，LI Haixia1，2. Coexistence states of unstirred Chemostat model with C-M functional response[J]. Computer Engineering and Applications, 2014, 50(7): 30-34.

姜洪领1，2，李海侠1，2. 带C-M反应项的非均匀恒化器模型的共存态[J]. 计算机工程与应用, 2014, 50(7): 30-34.

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Coexistence states of unstirred Chemostat model with C-M functional response

带C-M反应项的非均匀恒化器模型的共存态

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