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Nonlinear state-dependent impulsive system in fed-batch culture and its optimal control
A stochastic model for microbial fermentation process under Gaussian white noise environment
1. | School of Science, Dalian Jiaotong University,Dalian, MO 116028, China, China |
2. | School of Mathematical Sciences, Dalian University of Technology, Dalian, MO 116023, China |
3. | Department of Mathematics, The George Washington University,Washington DC 20052, United States |
4. | Department of Mathematics, Loyola Marymount University, Los Angeles CA 90045, United States |
References:
[1] |
I. Albert, R. Pouillot and J.-B. Denis, Stochastically modeling listeria monocytogenes growth in farm tank milk, Risk Analysis, 25 (2005), 1171-1185. |
[2] |
H. Biebl, K. Menzel, A. P. Zeng and W. Deckwer, Microbial production of 1,3-propanediol, Applied Microbiology and Biotechnology, 52 (1999), 297-298. |
[3] |
R. Bona and A. Moser, Modeling of l-glutamic acid production with Corynebacterium glutamicum under biotin limitation, Bioprocess Engineering, 17 (1997), 139-142. |
[4] |
C. Hartmann and A. Delgado, Numerical simulation of the mechanics of a yeast cell under high hydrostatic pressure, Journal of Biomechanics, 37 (2004), 977-987. |
[5] |
H. J. Henzler, Particle stress in bioreactors, Advances in Biochemical Engineering, 67 (2000), 35-82. |
[6] |
H. Holden, B. Øksendal, J. Ubøe and T. S. Zhang, Stochastic Partial Differential Equations-A Modeling, White Noise Functional Approach, 2nd edition, Springer-Verlag, New York, 2010.
doi: 10.1007/978-0-387-89488-1. |
[7] |
A. Kasperski, Modelling of cells bioenergetics, Acta Biotheoretica, 56 (2008), 233-247. |
[8] |
A. Kasperski and T. Miskiewicz, Optimization of pulsed feeding in a Baker's yeast process with dissolved oxygen concentration as a control parameter, Biochemical Engineering Journal, 40 (2008), 321-327. |
[9] |
Z. Kutalik, M. Razaz and J. Baranyi, Connection between stochastic and deterministic modelling of microbial growth, Journal of Theoretical Biology, 232 (2005), 285-299.
doi: 10.1016/j.jtbi.2004.08.013. |
[10] |
X. Li and X. Mao, Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation, Discrete and Continuous Dynamical Systems, 24 (2009), 523-545.
doi: 10.3934/dcds.2009.24.523. |
[11] |
B. Ø ksendal and A. Sulem, Applied Stochastic Control of Jump Diffusion, 2nd edition, Springer, Berlin, 2007.
doi: 10.1007/978-3-540-69826-5. |
[12] |
B. Ø ksendal, Stochastic Differential Equations, 6nd edition, Springer, Berlin, Heidelberg, New York, 2005. |
[13] |
H. J. Rehm and G. Reed, Microbial Fundamentals, Verlag Chemie, Weinheim, 1981. |
[14] |
K. Schügerl, Bioreaction Engineering: Reactions Involving Microorganisms and Cells: Fundamentals, Thermodynamics, Formal Kinetics, Idealized Reactor Types and Operation, Wiley, Chichester, 1987. |
[15] |
T. K. Soboleva, A. E. Filippov, A. B. Pleasants, R. J. Jones and G. A. Dykes, Stochastic modelling of the growth of a microbial population under changing temperature regimes, International Journal of Food Microbiology, 64 (2001), 317-323. |
[16] |
S. Suresh, N. S. Khan, V. C. Srivastava and I. M. Mishra, Kinetic modeling and sensitivity analysis of kinetic parameters for $l$-glutamic acid production using Corynebacterium glutamicum, International Journal of Chemical Reactor Engineering, 7 (2009), Article A89. |
[17] |
Y. Tian, A. Kasperski, K. Sun and Lansun Chen, Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect, BioSystems, 104 (2011), 77-86. |
[18] |
M. K. Toma, M. P. Rukilisha, J. J. Vanags, M. O. Zeltina, M. P. Leite, N. I. Galinina, U. E. Viesturs and R. P. Tengerdy, Inhibition of microbial growth and metabolism by excess turbulence, Biotechnology and Bioengineering, 38 (2000), 552-556. |
[19] |
L. Wang, Z. Xiu and E. Feng, A stochastic model of microbial bioconversion process in batch culture, International journal of Chemical reactor engineering, 9 (2011), Article A82. |
[20] |
L. Wang, Z. Xiu and E. Feng, Modeling nonlinear stochastic kinetic system and stochastic optimal control of microbial bioconversion process in batch culture, Nonlinear Analysis: Modelling and Control, 18 (2013), 99-111. |
show all references
References:
[1] |
I. Albert, R. Pouillot and J.-B. Denis, Stochastically modeling listeria monocytogenes growth in farm tank milk, Risk Analysis, 25 (2005), 1171-1185. |
[2] |
H. Biebl, K. Menzel, A. P. Zeng and W. Deckwer, Microbial production of 1,3-propanediol, Applied Microbiology and Biotechnology, 52 (1999), 297-298. |
[3] |
R. Bona and A. Moser, Modeling of l-glutamic acid production with Corynebacterium glutamicum under biotin limitation, Bioprocess Engineering, 17 (1997), 139-142. |
[4] |
C. Hartmann and A. Delgado, Numerical simulation of the mechanics of a yeast cell under high hydrostatic pressure, Journal of Biomechanics, 37 (2004), 977-987. |
[5] |
H. J. Henzler, Particle stress in bioreactors, Advances in Biochemical Engineering, 67 (2000), 35-82. |
[6] |
H. Holden, B. Øksendal, J. Ubøe and T. S. Zhang, Stochastic Partial Differential Equations-A Modeling, White Noise Functional Approach, 2nd edition, Springer-Verlag, New York, 2010.
doi: 10.1007/978-0-387-89488-1. |
[7] |
A. Kasperski, Modelling of cells bioenergetics, Acta Biotheoretica, 56 (2008), 233-247. |
[8] |
A. Kasperski and T. Miskiewicz, Optimization of pulsed feeding in a Baker's yeast process with dissolved oxygen concentration as a control parameter, Biochemical Engineering Journal, 40 (2008), 321-327. |
[9] |
Z. Kutalik, M. Razaz and J. Baranyi, Connection between stochastic and deterministic modelling of microbial growth, Journal of Theoretical Biology, 232 (2005), 285-299.
doi: 10.1016/j.jtbi.2004.08.013. |
[10] |
X. Li and X. Mao, Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation, Discrete and Continuous Dynamical Systems, 24 (2009), 523-545.
doi: 10.3934/dcds.2009.24.523. |
[11] |
B. Ø ksendal and A. Sulem, Applied Stochastic Control of Jump Diffusion, 2nd edition, Springer, Berlin, 2007.
doi: 10.1007/978-3-540-69826-5. |
[12] |
B. Ø ksendal, Stochastic Differential Equations, 6nd edition, Springer, Berlin, Heidelberg, New York, 2005. |
[13] |
H. J. Rehm and G. Reed, Microbial Fundamentals, Verlag Chemie, Weinheim, 1981. |
[14] |
K. Schügerl, Bioreaction Engineering: Reactions Involving Microorganisms and Cells: Fundamentals, Thermodynamics, Formal Kinetics, Idealized Reactor Types and Operation, Wiley, Chichester, 1987. |
[15] |
T. K. Soboleva, A. E. Filippov, A. B. Pleasants, R. J. Jones and G. A. Dykes, Stochastic modelling of the growth of a microbial population under changing temperature regimes, International Journal of Food Microbiology, 64 (2001), 317-323. |
[16] |
S. Suresh, N. S. Khan, V. C. Srivastava and I. M. Mishra, Kinetic modeling and sensitivity analysis of kinetic parameters for $l$-glutamic acid production using Corynebacterium glutamicum, International Journal of Chemical Reactor Engineering, 7 (2009), Article A89. |
[17] |
Y. Tian, A. Kasperski, K. Sun and Lansun Chen, Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect, BioSystems, 104 (2011), 77-86. |
[18] |
M. K. Toma, M. P. Rukilisha, J. J. Vanags, M. O. Zeltina, M. P. Leite, N. I. Galinina, U. E. Viesturs and R. P. Tengerdy, Inhibition of microbial growth and metabolism by excess turbulence, Biotechnology and Bioengineering, 38 (2000), 552-556. |
[19] |
L. Wang, Z. Xiu and E. Feng, A stochastic model of microbial bioconversion process in batch culture, International journal of Chemical reactor engineering, 9 (2011), Article A82. |
[20] |
L. Wang, Z. Xiu and E. Feng, Modeling nonlinear stochastic kinetic system and stochastic optimal control of microbial bioconversion process in batch culture, Nonlinear Analysis: Modelling and Control, 18 (2013), 99-111. |
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