| 带变消耗率和连续输入乙醇发酵数学模型研究 |
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| 作者单位： | ;1.黄淮学院数学科学系;2.信阳师范学院数学与信息科学学院 |
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| 摘 要： | 讨论了带变消耗率和连续输入乙醇发酵数学模型,利用线性扰动和Lyapunov方法研究了微生物灭绝平衡点的局部和全局稳定性及正平衡点的局部稳定性,并且得到正平衡点稳定性的阈值条件.最后利用Hopf分支理论,证明了在阈值条件下,从正平衡点周围分支出一个稳定的周期解.
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| 关 键 词： | 乙醇发酵 Lyapunov函数 Hopf分支 |
Studies on the Mathematical Model of Ethanol Fermentation with Variable Yield Rate |
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| Institution: | ,Department of Mathematics,Huanghuai University,College of Mathematics and Information Science,Xinyang Normal University |
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| Abstract: | A mathematical model for the ethanol fermentation with continuous input and variable yield was investigated. Using the small amplitude perturbation and Lyapunov function,the local and global stability of the boundary equilibrium and the positive equilibrium were discussed and the threshold conditions for the stability of the positive equilibrium were obtained. The Hopf bifurcation and the stability of the periodic solution created by the bifurcation were proved. |
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| Keywords: | ethanol fermentation Lyapunov function Hopf bifurcation |
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