| 李晓芳,冯恩民,连涵生.连续时滞对微生物连续培养过程振荡行为影响[J].,2011,(2):309-312 |
| 连续时滞对微生物连续培养过程振荡行为影响 |
| Effect of distributed time-delay on oscillation behaviors in microbial continuous culture |
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| DOI：10.7511/dllgxb201102027 |
| 中文关键词: 连续培养 时滞 Hopf分支 稳定性 周期解 |
| 英文关键词: continuous culture time-delay Hopf bifurcation stability period solution\@ |
| 基金项目:“九七三”国家重点基础研究发展计划资助项目(2007CB714304);威海市科技发展计划资助项目;哈尔滨工业大学(威海)研究基金资助项目(HIT(WH)2008009,HIT(WH)ZBQD201006). |
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| 中文摘要: |
| 以微生物歧化方法生产1,3-丙二醇的连续发酵为背景, 考虑乙酸和乙醇对微生物生长的抑制作用, 在细胞比生长速率中引入弱核连续时滞, 提出了一个五维连续时滞动力系统．将平均时滞的倒数看作参数, 研究了平均时滞对系统正平衡点局部稳定性的影响．运用Hopf分支的代数判据, 给出了存在Hopf分支的操作参数区域, 并数值模拟了分支的周期解及相图．最后讨论了系统的过渡行为． |
| 英文摘要: |
| Taking acetate and ethanol inhibition for microbe into account with the continuous fermentation by bio-dissimilation to produce 1,3-propanediol, the weak nuclear continuous time-delay is introduced into the specific cellular growth rate, and a five-dimensional distributed time-delay differential system is presented. Taking the inverse of the average time-delay as parameter, the effect of average time-delay on the local stability of the positive equilibrium(s) is discussed. The operating parameter region in which there exists Hopf bifurcation is given using the algebra criteria of Hopf bifurcation, and periodic solutions and phase diagram are numerically simulated. Finally, the transition behavior of the system is discussed. |
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