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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): 369-380.doi: 10.3969/j.issn.1005-3085.2015.03.006

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一类带B-D反应项的非均匀Chemostat模型正解的存在性和多解性

李海侠   

  1. 宝鸡文理学院数学与信息科学学院，宝鸡 721013
  • 收稿日期:2013-11-18 接受日期:2014-10-27 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    中央高校科研基本业务费 (GK201303008)；陕西省教育厅专项科研计划资助项目 (14JK1035)；宝鸡文理学院重点科研项目 (ZK15039).

Existence and Multiplicity of Positive Solutions for an Unstirred Chemostat Model with B-D Functional Response

LI Hai-xia   

  1. College of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013
  • Received:2013-11-18 Accepted:2014-10-27 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The Fundamental Research Fund for the Central Universities (GK201303008); the Scienfific Research Foundation of Shaanxi Educational Committee (14JK1035); the Key Research Program of Baoji University of Arts and Sciences (ZK15039).

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摘要： 本文研究一类带有Beddington-DeAngelis反应函数的非均匀Chemostat模型正平衡态解的存在性和多解性．利用分歧理论考察了共存解的全局结构，得到了正平衡态解存在的充分条件．进而讨论了正平衡态解的稳定性和多解性，运用线性算子的扰动理论和不动点指数理论给出了正平衡态的多解条件．结果表明质粒载体微生物的最大生长率对正平衡态解的稳定性和多解性有很大影响．

关键词: Chemostat模型, Beddington-DeAngelis反应函数, 分歧, 稳定性, 多解性

Abstract:

We investigate the existence and multiplicity of positive steady-state solutions to the unstirred Chemostat model with Beddington-DeAngelis functional response. The global structure of coexistence solutions is studied by the bifurcation theory. Sufficiently conditions for the existence of positive steady-state solutions are obtained. Furthermore, the stability and multiplicity of positive steady-state solutions are discussed. Conditions for the multiple existence of positive steady-state solutions are established by means of the perturbation theory for linear operators and the fixed point index theory. The results indicate that the maximal growth rate of the plasmid-bearing organism has an effect on the stability and multiplicity of positive steady-state solutions.

Key words: Chemostat model, Beddington-DeAngelis functional response, bifurcation, stabi-lity, multiplicity

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