Asymptotical stability of a nonlinear non-differentiable dynamic system in microbial continuous cultures

Advances in Difference Equations

Liping Pang¹  Enmin Feng¹  Jiajia Lv¹ 

[1] School of Mathematical Sciences, Dalian University of Technology, Dalian, China

关键词: nonlinear dynamic system;    equilibrium point;    tensor;    asymptotical stability;   

DOI  :  10.1186/s13662-017-1288-x

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY