文章基本信息

标题：Asymptotical stability of a nonlinear non-differentiable dynamic system in microbial continuous cultures
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作者：Jiajia Lv ; Liping Pang ; Enmin Feng 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2017
卷号：2017
期号：1
页码：256
DOI：10.1186/s13662-017-1288-x
语种：English
出版社：Hindawi Publishing Corporation
摘要：In this paper, we consider a nonlinear non-differentiable dynamic system in microbial continuous cultures involving all possible metabolic pathways of the inhibition mechanisms of 3-hydroxypropionaldehyde onto the cell growth and the transport systems of glycerol and 1,3-PD across the cell membrane. First, the existence of the equilibrium point of the system proved. And by numerical calculation, the equilibrium point of the system is obtained. Subsequently, we derive the local bounded properties of the Jacobian, tensor and Hessian matrices of the system. Finally, the local asymptotical stability of the system at equilibrium point is proved.
关键词：nonlinear dynamic system ; equilibrium point ; tensor ; asymptotical stability