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Journal of Applied Mathematics
Volume 2014, Article ID 925404, 8 pages
http://dx.doi.org/10.1155/2014/925404
Research Article

Robust Analysis and Parameters Identification of the Nonlinear Multistage Dynamical System in Batch Fermentation of Glycerol

1School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024, China
2Department of Biotechnology, Dalian University of Technology, Dalian, Liaoning 116012, China

Received 18 June 2014; Accepted 3 September 2014; Published 21 October 2014

Academic Editor: Henggui Zhang

Copyright © 2014 Xu Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper discusses a complex biological problem which is the fermentation of glycerol by Klebsiella pneumoniae in batch culture. We set up an improved multistage model involving the concentration of intracellular substances. Furthermore, the existence, uniqueness, and continuity of solutions with respect to the parameters are discussed. On the condition that glycerol and 1,3-propanediol are assumed to pass the cell membrane by passive diffusion coupled with facilitated transport, we take the relative errors between experimental data and computational values of the extracellular substances concentrations and the biological robustness of the intracellular substances concentrations as the performance index. Then we establish a parameter identification model and construct the particle swarm optimization algorithm to solve it. Finally, the numerical result shows that the improved model could describe the glycerol fermentation in batch culture well.