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论文类型：期刊论文
发表时间：2017-08-25
发表刊物：ADVANCES IN DIFFERENCE EQUATIONS
收录刊物：Scopus、SCIE
卷号：2017
期号：1
ISSN号：1687-1847
关键字：nonlinear dynamic system; equilibrium point; tensor; asymptotical stability
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.