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Modeling and identification of dynamical system with Genetic Regulation in batch fermentation of glycerol
1.  School of Mathematical Science, Dalian University of Technology, Linggong Road, Dalian, Liaoning 116024, China, China 
References:
[1] 
C. X. Gao, Z. T. Wang, E. M. Feng and Z. L. Xiu, Parameter identification and optimization of process for biodissimilation of glycerol to 1,3propanediol in batch culture,, \emph{Journal of Dalian University of Technology}, 46 (2006), 771. 
[2] 
Z. H. Gong, E. M. Feng and Z. L. Xiu, Identification of specific growth rate and optimization algorithm in microbial batch culture,, \emph{Journal of Dalian University of Technology}, 49 (2009), 611. 
[3] 
Z. G. Jiang, J. L. Yuan and E. M. Feng, Robust identification and its properties of nonlinear bilevel multistage dynamic system,, \emph{Applied Mathematics and Computation}, 219 (2013), 6979. doi: 10.1016/j.amc.2012.12.082. 
[4] 
H. Kitano, Biological robustness,, \emph{Nat. Rev. Genet.}, 5 (2004), 826. 
[5] 
D. H. Liu, H. J. Liu and K. K. Cheng, Research progress on the production of l,3propanediol by fermentation,, \emph{Journal of Microbiolog}, 4 (2000), 300. 
[6] 
C. Y. Liu, L. Yin, E. M. Feng and Z. L. Xiu, Modeling of microbial continuous fermentations and identifying of intracellular kinetic parameters,, \emph{Journal of Dalian University of Technology}, 51 (2011), 458. 
[7] 
Y. Q. Sun, W. T. Qi, H. Teng, Z. L. Xiu and A. P. Zeng, Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: concerning enzymecatalytic reductive pathway and transport of glycerol and 1,3propanediol across cell membrane,, \emph{Biochemical Engineering Journal, 38 (2008), 22. 
[8] 
Y. Q. Sun, Nonlinear Mathematical Simulation and Analysis of EnzymeEatalytic Kinetics and Genetic Regulation for Glycerol Dissimilation by Klebsiella Pneumoniae,, Dalian: Dalian university of technology, (2010). 
[9] 
L. Wang, J. X. Ye, E. M. Feng and Z. L. Xiu, An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification,, \emph{Nonlinear Analysis: Hybrid Systems}, 3 (2009), 455. doi: 10.1016/j.nahs.2009.03.003. 
[10] 
J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and Z. L. Xiu, Modelling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol,, \emph{Mathematical and Computer Modelling}, 54 (2011), 618. doi: 10.1016/j.mcm.2011.03.005. 
[11] 
J. Wang, Modelling and Optimization of a Class of Nonlinear EnzymeCatalysis Hybrid System,, Dalian: Dalian university of technology, (2012). 
[12] 
Z. L. Xiu and A. P. Zeng, Mathematical modeling of kinetics and research on multiplicity of glycerol bioconversion to 1,3propanediol,, \emph{Journal of Dalian University of Technology}, 40 (2000), 428. 
[13] 
A. P. Zeng, H. Biebl and et al., Multiple product and growth modeling of clostridium butyicum and Klebsiella pneumoniae in fermentation,, \emph{Biotechnol.}, 44 (1994), 902. 
[14] 
Y. D. Zhang, Y. J. Zhang and E. M. Feng, Robustness analysis of microbio continuous fermentation based on parallel computing,, \emph{Journal of Biomathematics}, 3 (2011), 524. 
[15] 
C. Zhou, H. B. Gao and L. Gao, Particle swarm optimization (PSO) algorithm 3,, \emph{Application Research of Computers}, 12 (2003), 7. 
show all references
References:
[1] 
C. X. Gao, Z. T. Wang, E. M. Feng and Z. L. Xiu, Parameter identification and optimization of process for biodissimilation of glycerol to 1,3propanediol in batch culture,, \emph{Journal of Dalian University of Technology}, 46 (2006), 771. 
[2] 
Z. H. Gong, E. M. Feng and Z. L. Xiu, Identification of specific growth rate and optimization algorithm in microbial batch culture,, \emph{Journal of Dalian University of Technology}, 49 (2009), 611. 
[3] 
Z. G. Jiang, J. L. Yuan and E. M. Feng, Robust identification and its properties of nonlinear bilevel multistage dynamic system,, \emph{Applied Mathematics and Computation}, 219 (2013), 6979. doi: 10.1016/j.amc.2012.12.082. 
[4] 
H. Kitano, Biological robustness,, \emph{Nat. Rev. Genet.}, 5 (2004), 826. 
[5] 
D. H. Liu, H. J. Liu and K. K. Cheng, Research progress on the production of l,3propanediol by fermentation,, \emph{Journal of Microbiolog}, 4 (2000), 300. 
[6] 
C. Y. Liu, L. Yin, E. M. Feng and Z. L. Xiu, Modeling of microbial continuous fermentations and identifying of intracellular kinetic parameters,, \emph{Journal of Dalian University of Technology}, 51 (2011), 458. 
[7] 
Y. Q. Sun, W. T. Qi, H. Teng, Z. L. Xiu and A. P. Zeng, Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: concerning enzymecatalytic reductive pathway and transport of glycerol and 1,3propanediol across cell membrane,, \emph{Biochemical Engineering Journal, 38 (2008), 22. 
[8] 
Y. Q. Sun, Nonlinear Mathematical Simulation and Analysis of EnzymeEatalytic Kinetics and Genetic Regulation for Glycerol Dissimilation by Klebsiella Pneumoniae,, Dalian: Dalian university of technology, (2010). 
[9] 
L. Wang, J. X. Ye, E. M. Feng and Z. L. Xiu, An improved model for multistage simulation of glycerol fermentation in batch culture and its parameter identification,, \emph{Nonlinear Analysis: Hybrid Systems}, 3 (2009), 455. doi: 10.1016/j.nahs.2009.03.003. 
[10] 
J. Wang, J. X. Ye, E. M. Feng, H. C. Yin and Z. L. Xiu, Modelling and identification of a nonlinear hybrid dynamical system in batch fermentation of glycerol,, \emph{Mathematical and Computer Modelling}, 54 (2011), 618. doi: 10.1016/j.mcm.2011.03.005. 
[11] 
J. Wang, Modelling and Optimization of a Class of Nonlinear EnzymeCatalysis Hybrid System,, Dalian: Dalian university of technology, (2012). 
[12] 
Z. L. Xiu and A. P. Zeng, Mathematical modeling of kinetics and research on multiplicity of glycerol bioconversion to 1,3propanediol,, \emph{Journal of Dalian University of Technology}, 40 (2000), 428. 
[13] 
A. P. Zeng, H. Biebl and et al., Multiple product and growth modeling of clostridium butyicum and Klebsiella pneumoniae in fermentation,, \emph{Biotechnol.}, 44 (1994), 902. 
[14] 
Y. D. Zhang, Y. J. Zhang and E. M. Feng, Robustness analysis of microbio continuous fermentation based on parallel computing,, \emph{Journal of Biomathematics}, 3 (2011), 524. 
[15] 
C. Zhou, H. B. Gao and L. Gao, Particle swarm optimization (PSO) algorithm 3,, \emph{Application Research of Computers}, 12 (2003), 7. 
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