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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.

Linked References

  1. A. Reimann, H. Biebl, and W.-D. Deckwer, “Production of 1,3-propanediol by Clostridium butyricum in continuous culture with cell recycling,” Applied Microbiology and Biotechnology, vol. 49, no. 4, pp. 359–363, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. T. Homann, C. Tag, H. Biebl, W.-D. Deckwer, and B. Schink, “Fermentation of glycerol to 1,3-propanediol by Klebsiella and Citrobacter strains,” Applied Microbiology and Biotechnology, vol. 33, no. 2, pp. 121–126, 1990. View at Google Scholar · View at Scopus
  3. H. Biebl, K. Menzel, A.-P. Zeng, and W.-D. Deckwer, “Microbial production of 1,3-propanediol,” Applied Microbiology and Biotechnology, vol. 52, no. 3, pp. 289–297, 1999. View at Publisher · View at Google Scholar · View at Scopus
  4. K. Menzel, A.-P. Zeng, and W.-D. Deckwer, “High concentration and productivity of 1,3-propanediol from continuous fermentation of glycerol by Klebsiella pneumoniae,” Enzyme and Microbial Technology, vol. 20, no. 2, pp. 82–86, 1997. View at Publisher · View at Google Scholar · View at Scopus
  5. A.-P. Zeng and W.-D. Deckwer, “A kinetic model for substrate and energy consumption of microbial growth under substrate-sufficient conditions,” Biotechnology Progress, vol. 11, no. 1, pp. 71–79, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. L. Xiu and A. P. Zeng, “Mathematical modelling of kineti cs and research on multiplicity of glycerol bioconversion to 1 ,3-propanediol,” Journal of Dalian University of Technology, vol. 40, pp. 428–433, 2000. View at Google Scholar
  7. C. Gao, E. Feng, Z. Wang, and Z. Xiu, “Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 476–484, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Y. Q. Sun, W. T. Qi, H. Teng, Z. L. Xiu, and A. P. Zeng, “Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane,” Biochemical Engineering Journal, vol. 38, no. 1, pp. 22–32, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Wang, J. Ye, E. Feng, H. Yin, and Z. Xiu, “Modeling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol,” Mathematical and Computer Modelling, vol. 54, no. 1-2, pp. 618–624, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. C. X. Gao, Z. T. Wang, E. M. Feng, and Z. L. Xiu, “Parameter identification and optimization of process for bio-dissimilation of glycerol to 1,3-propanediol in batch culture,” Journal of Dalian University of Technology, vol. 46, pp. 771–774, 2006. View at Google Scholar
  11. L. Wang, J. Ye, E. Feng, and Z. Xiu, “An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 4, pp. 455–462, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. J. Song, J. Q. Lin, Y. Jin et al., “A new population growth model based on the time dependent changes of the specific growth rate,” Microbiology, vol. 34, pp. 836–838, 2007. View at Google Scholar
  13. Z. Bing, L. B. Jia, and Y. Lei, “Progress of biological robustness,” Acta Biophysica Sinica, vol. 23, pp. 357–363, 2007. View at Google Scholar
  14. H. Kitano, “Biological robustness,” Nature Reviews Genetics, vol. 5, no. 11, pp. 826–837, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. H. Kitano, “Towards a theory of biological robustness,” Molecular Systems Biology, vol. 3, article 137, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Wang, J. Ye, E. Feng, H. Yin, and B. Tan, “Complex metabolic network of glycerol fermentation by Klebsiella pneumoniae and its system identification via biological robustness,” Nonlinear Analysis: Hybrid Systems, vol. 5, no. 1, pp. 102–112, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Zhang, E. Feng, and Z. Xiu, “Robust analysis of hybrid dynamical systems for 1,3-propanediol transport mechanisms in microbial continuous fermentation,” Mathematical and Computer Modelling, vol. 54, no. 11-12, pp. 3164–3171, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. J. Kennedy and R. Eberhart, Swarm Intelligence, Academic Press, New York, NY, USA, 2001.
  19. H. Kitano, “Violations of robustness trade-offs,” Molecular Systems Biology, vol. 6, no. 1, article 384, 2010. View at Google Scholar
  20. M. Perc and M. Marhl, “Sensitivity and flexibility of regular and chaotic calcium oscillations,” Biophysical Chemistry, vol. 104, no. 2, pp. 509–522, 2003. View at Publisher · View at Google Scholar · View at Scopus
  21. M. Perc and M. Marhl, “Noise enhances robustness of intracellular Ca2+ oscillations,” Physics Letters A, vol. 316, no. 5, pp. 304–310, 2003. View at Publisher · View at Google Scholar · View at Scopus
  22. N. Barkai and S. Leibler, “Robustness in simple biochemical networks,” Nature, vol. 387, no. 6636, pp. 913–917, 1997. View at Publisher · View at Google Scholar · View at Scopus
  23. U. Alon, M. G. Surette, N. Barkai, and S. Leibler, “Robustness in bacterial chemotaxis,” Nature, vol. 397, no. 6715, pp. 168–171, 1999. View at Publisher · View at Google Scholar · View at Scopus
  24. D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J. Watts, “Network robustness and fragility: percolation on random graphs,” Physical Review Letters, vol. 85, pp. 5468–5471, 2000. View at Publisher · View at Google Scholar · View at Scopus