带变消耗率和连续输入乙醇发酵数学模型研究  

Studies on the Mathematical Model of Ethanol Fermentation with Variable Yield Rate

作　　者：赵中[1] 杨金根[2] 庞留勇[1] 

机构地区：[1]黄淮学院数学科学系,河南驻马店463000 [2]信阳师范学院数学与信息科学学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2016年第2期161-164,170,共5页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11371164);国家自然科学基金河南省人才培养联合基金项目(U1304104);河南省高校科技创新人才支持计划(15HASTIT014);河南省青年骨干教师计划(2013GGJS-214)

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.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.

关 键 词：乙醇发酵 LYAPUNOV函数 HOPF分支 

分 类 号：O175.2[理学—数学]