Existence and stability of positive solutions for an unstirred chemostat model with toxins

LI Haixia

doi:10.13471/j.cnki.acta.snus.2019.09.23.2019A073

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Existence and stability of positive solutions for an unstirred chemostat model with toxins

Research articles | 更新时间：2023-12-08

- Existence and stability of positive solutions for an unstirred chemostat model with toxins
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 60, Issue 3, Pages: 167-173(2021)
- 作者机构：
  
  宝鸡文理学院数学与信息科学学院，陕西宝鸡 721013
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2019.09.23.2019A073
  CLC： O175.26
- Published：25 May 2021，
  
  Published Online：08 January 2021，
  
  Received：23 September 2019，
  
  Accepted：18 September 2020
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李海侠.一类具有毒素的非均匀chemostat模型正解的存在性和稳定性[J].中山大学学报(自然科学版),2021,60(03):167-173.

LI Haixia.Existence and stability of positive solutions for an unstirred chemostat model with toxins[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(03):167-173.
李海侠.一类具有毒素的非均匀chemostat模型正解的存在性和稳定性[J].中山大学学报(自然科学版),2021,60(03):167-173. DOI： 10.13471/j.cnki.acta.snus.2019.09.23.2019A073.

LI Haixia.Existence and stability of positive solutions for an unstirred chemostat model with toxins[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2021,60(03):167-173. DOI： 10.13471/j.cnki.acta.snus.2019.09.23.2019A073.

摘要

研究了一类具有毒素的非均匀chemostat食物链模型。利用最大值原理和上下解方法给出了正解的先验估计。接着运用简单特征值的分歧理论探讨了正解的全局分支，得到了正解存在的充要条件。最后采用线性算子的扰动理论和分歧解的稳定性理论讨论了正分歧解的稳定性。研究结果表明在毒素的影响和适当条件下物种能够共存且正解稳定。

Abstract

A food chain unstirred chemostat model with toxins is investigated. A priori estimate of positive solutions is given by the maximum principle and the super and sub-solution method. Then by using the bifurcation theory of simple eigenvalues， the global branch of positive solutions is studied， and the sufficient and necessary conditions for the existence of positive solutions are obtained. Finally， the stability of positive bifurcating solutions is discussed by means of the perturbation theory of linear operators and the stability theory of bifurcation solutions. The research results indicate that the species can coexist and positive solutions are stable under the influence of toxins and appropriate conditions.

关键词

非均匀chemostat模型分歧理论全局分支稳定性

Keywords

unstirred chemostat modelbifurcation theoryglobal branchstability

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