| 微生物连续发酵模型及正解的存在性与稳定性分析 |
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| 引用本文： | 王诗云,杨淑辉,叶剑雄,冯恩民. 微生物连续发酵模型及正解的存在性与稳定性分析[J]. 生物数学学报, 2010, 0(1): 113-121 |
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| 作者姓名： | 王诗云 杨淑辉 叶剑雄 冯恩民 |
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| 作者单位： | 沈阳航空航天大学理学院;沈阳师范大学计算机与数学基础教学部;大连理工大学数学科学学院; |
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| 基金项目： | 沈阳航空工业学院青年自选课题(200923Y) |
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| 摘 要： | 本文引入一个新的非线性动力系统,描述Klebsiella pneumoniae以甘油为底物发酵生成1,3-丙二醇的过程.此模型考虑了细胞内物质的浓度,研究甘油主动运输及1,3-丙二醇被动扩散的跨膜方式.证明模型解的存在唯一性,通过引入微分包含和上哈密尔顿函数证明正解的存在性.此外,以稀释速率0.1为例计算平衡点,并对系统的稳定性做出分析.
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| 关 键 词： | 微生物连续发酵 正解 多稳态 稳定性 |
Existence of Positive Solution and Stability Analysis of a New Model in Microbial Continuous Culture |
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| WANG Shi-yun YANG Shu-hui YE Jian-xiong FENG En-min. Existence of Positive Solution and Stability Analysis of a New Model in Microbial Continuous Culture[J]. Journal of Biomathematics, 2010, 0(1): 113-121 |
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| Authors: | WANG Shi-yun YANG Shu-hui YE Jian-xiong FENG En-min |
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| Affiliation: | WANG Shi-yun~1 YANG Shu-hui~2 YE Jian-xiong~3 FENG En-min~3 (1 School of Science,Shenyang Institute of Aeronautical Engineering,Shenyang Liaoning 110136 China,2 Department of Computer , Mathematics Teaching,Shenyang Normal University,Shenyang Liaoning 110034 China,3 School of Mathematical Science,Dalian University of Technology,Dalian Liaoning 116024 China) |
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| Abstract: | In this study,a new model is proposed to describe the conversion of glycerol to 1,3-propanediol by Klebsiella pneumoniae,in which the changes of concentrations of intracellular substances are taken into consideration.We consider the case that glycerol passes the cell membrane by active transport and 1,3-propanediol by passive diffusion.We firstly study the existence and uniqueness of the solution to the model,and then prove the existence of positive solution in the light of differential inclusion.The equili... |
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| Keywords: | Microbial continuous culture Positive solution Multiple steady states Stability |
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