The Strong Stability of Optimal Nonlinear Dynamical System in Batch Fermentation

Abstract

For the bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae, the nonlinear dynamical system of the complex metabolism in microbial batch fermentation is studied in this study. Since the analytical solution and equilibrium point cannot be found for the nonlinear dynamical system of batch fermentation, the system stability cannot be analyzed using general methods. Therefore, in this study, the stability of the system is analyzed from another angle. We present the corresponding linear variational system for the solution to the nonlinear dynamical system of complex metabolism. In addition, the boundedness of fundamental matrix solutions for the linear variational system is obtained. With this in mind, strong stability with respect to the perturbation of the initial state vector is proved for the nonlinear dynamical system of the complex metabolism.