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.

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