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Date:2019-03-11

Indexed by:Journal Article

Date of Publication:2017-08-25

Journal:ADVANCES IN DIFFERENCE EQUATIONS

Included Journals:SCIE、Scopus

Volume:2017

Issue:1

ISSN:1687-1847

Key Words:nonlinear dynamic system; equilibrium point; tensor; asymptotical stability

Abstract: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.