메뉴 건너뛰기




Volumn 46, Issue 2, 2009, Pages 303-321

Analysis of a chemostat model with variable yield coefficient: Tessier kinetics

Author keywords

Bifurcation; Bioreactors; Continuous culture; Nonlinear dynamics; Reaction engineering; Stability; Variable yield

Indexed keywords


EID: 67650586560     PISSN: 02599791     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10910-008-9463-7     Document Type: Article
Times cited : (12)

References (45)
  • 2
    • 0001639179 scopus 로고
    • The growth of bacterial culture
    • J. Monod 1949 The growth of bacterial culture Annu. Rev. Microbiol. 3 371 394
    • (1949) Annu. Rev. Microbiol. , vol.3 , pp. 371-394
    • Monod, J.1
  • 4
    • 0001894285 scopus 로고
    • Kinetics of bacterial growth: Relationship between population density and specific growth rate of continuous cultures
    • D.E. Contois 1959 Kinetics of bacterial growth: relationship between population density and specific growth rate of continuous cultures J. Gen. Microbiol. 21 40 50
    • (1959) J. Gen. Microbiol. , vol.21 , pp. 40-50
    • Contois, D.E.1
  • 5
    • 84984082223 scopus 로고
    • A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrate
    • J.F. Andrews 1968 A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrate Biotechnol. Bioeng. 10 6 707 724
    • (1968) Biotechnol. Bioeng. , vol.10 , Issue.6 , pp. 707-724
    • Andrews, J.F.1
  • 6
    • 0242470179 scopus 로고    scopus 로고
    • Improvement of chemostat performance via nonlinear oscillations, Part 2. Extension to other systems
    • A. Balakrishnan R.Y.K. Yang 1998 Improvement of chemostat performance via nonlinear oscillations. Part 2. Extension to other systems ACH-Models Chem. 135 1-2 1 18 (Pubitemid 128771622)
    • (1998) ACH - Models in Chemistry , vol.135 , Issue.1-2 , pp. 1-18
    • Balakrishnan, A.1    Yang, R.Y.K.2
  • 7
    • 0029240383 scopus 로고
    • Performance enhancement and optimization of chemostat cascades
    • C.-C. Chen C. Hwang R.Y.K. Yang 1995 Performance enhancement and optimization of chemostat cascades Chem. Eng. Sci. 50 3 485 494
    • (1995) Chem. Eng. Sci. , vol.50 , Issue.3 , pp. 485-494
    • Chen, C.-C.1    Hwang, C.2    Yang, R.Y.K.3
  • 8
    • 1642545135 scopus 로고    scopus 로고
    • Performance improvement of activated sludge wastewater treatment by nonlinear natural oscillations
    • S. Jianqiang A.K. Ray 2000 Performance improvement of activated sludge wastewater treatment by nonlinear natural oscillations Chem. Eng. Technol. 23 12 1115 1122
    • (2000) Chem. Eng. Technol. , vol.23 , Issue.12 , pp. 1115-1122
    • Jianqiang, S.1    Ray, A.K.2
  • 9
    • 0006118930 scopus 로고
    • Performance improvement of a chemical reactor by non-linear natural oscillations
    • A.J. Ray 1995 Performance improvement of a chemical reactor by non-linear natural oscillations Chem. Eng. J. 59 169 175
    • (1995) Chem. Eng. J. , vol.59 , pp. 169-175
    • Ray, A.J.1
  • 10
    • 0027299661 scopus 로고
    • Improvement of chemostat performance via nonlinear oscillations. Part 1: Operation strategy
    • DOI 10.1007/BF00369037
    • R.Y.K. Yang J. Su 1993 Improvement of chemostat performance via nonlinear oscillations. Part 1: operation strategy Bioprocess Eng. 9 97 102 (Pubitemid 23156462)
    • (1993) Bioprocess Engineering , vol.9 , Issue.2-3 , pp. 97-102
    • Yang, R.Y.K.1    Su, J.2
  • 11
    • 33644969271 scopus 로고    scopus 로고
    • Evaluating the performance of a cascade of two bioreactors
    • 10.1016/j.ces.2005.12.007
    • M.I. Nelson H.S. Sidhu 2006 Evaluating the performance of a cascade of two bioreactors Chem. Eng. Sci. 61 10 3159 3166 10.1016/j.ces.2005.12.007
    • (2006) Chem. Eng. Sci. , vol.61 , Issue.10 , pp. 3159-3166
    • Nelson, M.I.1    Sidhu, H.S.2
  • 12
    • 0041354063 scopus 로고    scopus 로고
    • The double-substrate growth kinetics of Sulfolobus solfataricus a thermophilic sulfur-removing archeabacterium
    • M. Sömezişik D. Tanyolaç S. Şeker A. Tanyolaç 1998 The double-substrate growth kinetics of Sulfolobus solfataricus a thermophilic sulfur-removing archeabacterium Biochem. Eng. J. 1 243 248
    • (1998) Biochem. Eng. J. , vol.1 , pp. 243-248
    • Sömezişik, M.1    Tanyolaç, D.2    Şeker, S.3    Tanyolaç, A.4
  • 14
    • 0036751989 scopus 로고    scopus 로고
    • Multiple substrate growth kinetics of Leptothrix discophora SP-6
    • DOI 10.1021/bp0255098
    • N. Yurt J. Sears Z. Lewandowski 2002 Multiple substrate growth kinetics of Leptothrix disophora SP-6 Biotechnol. Prog. 18 994 1002 (Pubitemid 35211920)
    • (2002) Biotechnology Progress , vol.18 , Issue.5 , pp. 994-1002
    • Yurt, N.1    Sears, J.2    Lewandowski, Z.3
  • 15
    • 0037413418 scopus 로고    scopus 로고
    • The double substrate growth kinetics of Pseudomonas aeruginosa
    • DOI 10.1016/S0141-0229(02)00246-6, PII S0141022902002466
    • H. Beyenal S.N. Chen Z. Lewandowski 2003 The double substrate growth kinetics of Pseudomonas aeruginosa Enzyme Microb. Technol. 32 92 98 (Pubitemid 35447747)
    • (2003) Enzyme and Microbial Technology , vol.32 , Issue.1 , pp. 92-98
    • Beyenal, H.1    Chen, S.N.2    Lewandowski, Z.3
  • 16
    • 0019203178 scopus 로고
    • The effect of the specific growth rate and yield expressions on the existence of oscillatory behaviour of a continuous fermentation model
    • P.S. Crooke C.-J. Wei R.D. Tanner 1980 The effect of the specific growth rate and yield expressions on the existence of oscillatory behaviour of a continuous fermentation model Chem. Eng. Commun. 6 6 333 347
    • (1980) Chem. Eng. Commun. , vol.6 , Issue.6 , pp. 333-347
    • Crooke, P.S.1    Wei, C.-J.2    Tanner, R.D.3
  • 17
    • 0009658607 scopus 로고
    • The effect of extracellular variables on the stability of the continuous baker's yeast-ethanol fermentation process
    • C.K. Essajee R.D. Tanner 1979 The effect of extracellular variables on the stability of the continuous baker's yeast-ethanol fermentation process Process Biochem. 14 16 25
    • (1979) Process Biochem. , vol.14 , pp. 16-25
    • Essajee, C.K.1    Tanner, R.D.2
  • 18
    • 0019900037 scopus 로고
    • Hopf bifurcations for a variable yield continuous fermentation model
    • P.S. Crooke R.D. Tanner 1982 Hopf bifurcations for a variable yield continuous fermentation model Int. J. Eng. Sci. 20 3 439 443
    • (1982) Int. J. Eng. Sci. , vol.20 , Issue.3 , pp. 439-443
    • Crooke, P.S.1    Tanner, R.D.2
  • 19
    • 0019927659 scopus 로고
    • THEORETICAL INVESTIGATIONS of DYNAMIC BEHAVIOR of ISOTHERMAL CONTINUOUS STIRRED TANK BIOLOGICAL REACTORS.
    • DOI 10.1016/0009-2509(82)80098-5
    • P. Agrawal C. Lee H.C. Lim D. Ramkrishna 1982 Theoretical investigations of dynamic behaviour of isothermal continuous stirred tank biological reactors Chem. Eng. Sci. 37 453 462 (Pubitemid 12509201)
    • (1982) Chemical Engineering Science , vol.37 , Issue.3 , pp. 453-462
    • Agrawal, P.1    Lee, C.2    Lim, H.C.3    Ramkrishna, D.4
  • 20
    • 0242338454 scopus 로고    scopus 로고
    • Self-forcing of a chemostat with self-sustained oscillations for productivity enhancement
    • DOI 10.1080/00986440214998
    • A. Balakrishnan R.Y.K. Yang 2002 Self-forcing of a chemostat with self-sustained oscillations for product enhancement Chem. Eng. Commun. 189 11 1569 1585 (Pubitemid 37343234)
    • (2002) Chemical Engineering Communications , vol.189 , Issue.11 , pp. 1569-1585
    • Balakrishnan, A.1    Yang, R.Y.K.2
  • 21
    • 67650634539 scopus 로고    scopus 로고
    • Analysis of a chemostat model with variable yield coefficient
    • M.I. Nelson H.S. Sidhu 2005 Analysis of a chemostat model with variable yield coefficient J. Math. Chem. 38 4 605 615
    • (2005) J. Math. Chem. , vol.38 , Issue.4 , pp. 605-615
    • Nelson, M.I.1    Sidhu, H.S.2
  • 22
    • 34250841128 scopus 로고    scopus 로고
    • Output regulation of self-oscillating biosystems: Model-based proportional-integral/proportional-integral-derivative (PI/PID) control approaches
    • DOI 10.1021/ie061314j
    • W. Wu H.-Y. Chang 2007 Output regulation of self-oscillating biosystems: model-based proportional-integral/proportional-integral-derivative (pi/pid) control approaches Ind. Eng. Chem. Res. 46 12 4282 4288 (Pubitemid 46982439)
    • (2007) Industrial and Engineering Chemistry Research , vol.46 , Issue.12 , pp. 4282-4288
    • Wu, W.1    Chang, H.-Y.2
  • 23
    • 13444287117 scopus 로고
    • Limit cycles in a continuous fermentation model
    • X.-C. Huang 1990 Limit cycles in a continuous fermentation model J. Math. Chem. 5 287 296
    • (1990) J. Math. Chem. , vol.5 , pp. 287-296
    • Huang, X.-C.1
  • 24
    • 0037376825 scopus 로고    scopus 로고
    • Multiple limit cycles in the chemostat with variable yield
    • DOI 10.1016/S0025-5564(02)00214-6, PII S0025556402002146
    • S.S. Pilyugin P. Waltman 2003 Multiple limit cycles in the chemostat with variable yield Math. Biosci. 182 151 166 (Pubitemid 36330981)
    • (2003) Mathematical Biosciences , vol.182 , Issue.2 , pp. 151-166
    • Pilyugin, S.S.1    Waltman, P.2
  • 25
    • 37549018909 scopus 로고    scopus 로고
    • Complex dynamics of a chemostat with variable yield and periodically impulsive perturbation on the substrate
    • S. Sun L. Chen 2008 Complex dynamics of a chemostat with variable yield and periodically impulsive perturbation on the substrate J. Math. Chem. 43 1 338 349
    • (2008) J. Math. Chem. , vol.43 , Issue.1 , pp. 338-349
    • Sun, S.1    Chen, L.2
  • 26
    • 23844465610 scopus 로고    scopus 로고
    • Relative positions of limit cycles in the continuous culture vessel with variable yield
    • DOI 10.1007/s10910-005-4837-6
    • L. Zhu X. Huang 2005 Relative positions of limit cycles in the continuous culture vessel with variable yield J. Math. Chem. 38 2 119 128 (Pubitemid 41167745)
    • (2005) Journal of Mathematical Chemistry , vol.38 , Issue.2 , pp. 119-128
    • Zhu, L.1    Huang, X.2
  • 27
    • 29244466456 scopus 로고    scopus 로고
    • Multiple limit cycles in a continuous culture vessel with variable yield
    • L. Zhu X. Huang 2006 Multiple limit cycles in a continuous culture vessel with variable yield Nonlinear Anal. 64 887 894
    • (2006) Nonlinear Anal. , vol.64 , pp. 887-894
    • Zhu, L.1    Huang, X.2
  • 28
    • 25144493055 scopus 로고    scopus 로고
    • A three-dimensional chemostat with quadratic yields
    • DOI 10.1007/s10910-005-6476-3
    • X. Huang L. Zhu 2005 A three-dimensional chemostat with quadratic yields J. Math. Chem. 38 3 399 412 (Pubitemid 41350561)
    • (2005) Journal of Mathematical Chemistry , vol.38 , Issue.3 , pp. 399-412
    • Huang, X.1    Zhu, L.2
  • 29
    • 33644850240 scopus 로고    scopus 로고
    • Competition in the bioreactor with general quadratic yields when one competitor produces a toxin
    • X. Huang Y. Wang L. Zhu 2006 Competition in the bioreactor with general quadratic yields when one competitor produces a toxin J. Math. Chem. 39 2 281 294
    • (2006) J. Math. Chem. , vol.39 , Issue.2 , pp. 281-294
    • Huang, X.1    Wang, Y.2    Zhu, L.3
  • 30
    • 33750086048 scopus 로고    scopus 로고
    • Limit cycles in a chemostat with general variable yields and growth rates
    • DOI 10.1016/j.nonrwa.2005.06.007, PII S1468121805001008
    • X. Huang L. Zhu E.H.C. Chang 2007 Limit cycles in a chemostat with general variable yields and growth rates Nonlinear Anal.: Real World Appl. 8 165 173 (Pubitemid 44584790)
    • (2007) Nonlinear Analysis: Real World Applications , vol.8 , Issue.1 , pp. 165-173
    • Huang, X.1    Zhu, L.2    Chang, E.H.C.3
  • 31
    • 34548423242 scopus 로고    scopus 로고
    • A note on competition in the bioreactor with toxin
    • X. Huang L. Zhu 2007 A note on competition in the bioreactor with toxin J. Math. Chem. 42 3 645 659
    • (2007) J. Math. Chem. , vol.42 , Issue.3 , pp. 645-659
    • Huang, X.1    Zhu, L.2
  • 32
    • 33845596338 scopus 로고    scopus 로고
    • Limit cycles in chemostat with constant yields
    • DOI 10.1016/j.mcm.2006.09.002, PII S089571770600327X
    • L. Zhu 2007 Limit cycles in chemostat with constant yields Math. Comput. Model. 45 927 932 (Pubitemid 44937554)
    • (2007) Mathematical and Computer Modelling , vol.45 , Issue.7-8 , pp. 927-932
    • Zhu, L.1
  • 33
    • 33846642733 scopus 로고    scopus 로고
    • Bifurcation for a functional yield chemostat when one competitor produces a toxin
    • L. Zhu X. Huang H. Su 2007 Bifurcation for a functional yield chemostat when one competitor produces a toxin J. Math. Anal. Appl. 329 891 903
    • (2007) J. Math. Anal. Appl. , vol.329 , pp. 891-903
    • Zhu, L.1    Huang, X.2    Su, H.3
  • 34
    • 33745125384 scopus 로고    scopus 로고
    • The 3-D Hopf bifurcation in bio-reactor when one competitor produces a toxin
    • DOI 10.1016/j.nonrwa.2005.10.006, PII S1468121805001422
    • X. Huang L. Zhu E.H.C. Chang 2006 The 3-D Hopf bifurcation in bio-reactor when one competitor produces a toxin Nonlinear Anal.: Real World Appl. 7 1167 1177 (Pubitemid 43903687)
    • (2006) Nonlinear Analysis: Real World Applications , vol.7 , Issue.5 , pp. 1167-1177
    • Huang, X.1    Zhu, L.2    Chang, E.H.C.3
  • 35
    • 0021794735 scopus 로고
    • On the parameter-space classification of the dynamic behaviour of a continuous microbial flow reactor
    • S. Suzuki K. Shimizu M. Matsubara 1985 On the parameter-space classification of the dynamic behaviour of a continuous microbial flow reactor Chem. Eng. Commun. 33 325 335
    • (1985) Chem. Eng. Commun. , vol.33 , pp. 325-335
    • Suzuki, S.1    Shimizu, K.2    Matsubara, M.3
  • 36
    • 0022045458 scopus 로고
    • CONDITIONS for the PHASE-PLANE ANALYSIS of FEEDBACK CONTROL of CHEMOSTAT.
    • K. Shimizu M. Matsubara 1985 Conditions for the phase-plane analysis of feedback control of chemostat Biotechnol. Bioeng. 27 4 519 524 (Pubitemid 15479981)
    • (1985) Biotechnology and Bioengineering , vol.27 , Issue.4 , pp. 519-524
    • Kazuyuki, S.1    Masakazu, M.2
  • 38
    • 33847132007 scopus 로고    scopus 로고
    • Reducing the emission of pollutants in food processing wastewaters
    • 10.1016/j.cep.2006.04.012
    • M.I. Nelson H.S. Sidhu 2007 Reducing the emission of pollutants in food processing wastewaters Chem. Eng. Process. 46 5 429 436 10.1016/j.cep.2006.04. 012
    • (2007) Chem. Eng. Process. , vol.46 , Issue.5 , pp. 429-436
    • Nelson, M.I.1    Sidhu, H.S.2
  • 39
    • 63149123732 scopus 로고    scopus 로고
    • Reducing the emission of pollutants in industrial wastewater through the use of membrane reactors
    • ed. by R.J. Hosking, E. Venturino (Birkhäuser, Basel)
    • M.I. Nelson, X.D. Chen, H.S. Sidhu, Reducing the emission of pollutants in industrial wastewater through the use of membrane reactors, in Aspects of Mathematical Modelling, ed. by R.J. Hosking, E. Venturino (Birkhäuser, Basel, 2008), pp. 95-107
    • (2008) Aspects of Mathematical Modelling , pp. 95-107
    • Nelson, M.I.1    Chen, X.D.2    Sidhu, H.S.3
  • 40
    • 44249098101 scopus 로고    scopus 로고
    • A fundamental analysis of continuous flow bioreactor models and membrane reactor models to process industrial wastewaters
    • M.I. Nelson E. Balakrishnan H.S. Sidhu X.D. Chen 2008 A fundamental analysis of continuous flow bioreactor models and membrane reactor models to process industrial wastewaters Chem. Eng. J. 140 1-3 521 528
    • (2008) Chem. Eng. J. , vol.140 , Issue.13 , pp. 521-528
    • Nelson, M.I.1    Balakrishnan, E.2    Sidhu, H.S.3    Chen, X.D.4
  • 41
    • 0029370722 scopus 로고
    • Periodical operation of continuous bioreactor
    • H.-S. Liu S.-C. Wu 1995 Periodical operation of continuous bioreactor J. Chin. Inst. Chem. Eng. 26 5 233 243
    • (1995) J. Chin. Inst. Chem. Eng. , vol.26 , Issue.5 , pp. 233-243
    • Liu, H.-S.1    Wu, S.-C.2
  • 42
    • 0031629330 scopus 로고    scopus 로고
    • Theoretical analysis of frequency response in continuous bioreactor
    • H.-S. Liu S.-C. Wu S.-C. Lin 1998 Theoretical analysis of frequency response in continuous bioreactor Chem. Eng. Commun. 164 13 34 (Pubitemid 128610057)
    • (1998) Chemical Engineering Communications , vol.164 , pp. 13-34
    • Liu, H.-S.1    Wu, S.-C.2    Lin, S.-C.3
  • 45
    • 0002184017 scopus 로고
    • A method for the complete qualitative analysis of two coupled ordinary differential equations dependent on three parameters
    • B.F. Gray M.J. Roberts 1988 A method for the complete qualitative analysis of two coupled ordinary differential equations dependent on three parameters Proc. Roy. Soc. A, 416 361 389
    • (1988) Proc. Roy. Soc. A , vol.416 , pp. 361-389
    • Gray, B.F.1    Roberts, M.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.