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Volumn 2, Issue 3, 2009, Pages 321-338

Stability and Hopf bifurcation of a delay differential system in microbial continuous culture

Author keywords

Hopf bifurcation; periodic solution; phase plane; Stability; time delay

Indexed keywords


EID: 84863116089     PISSN: 17935245     EISSN: 17937159     Source Type: Journal    
DOI: 10.1142/S179352450900073X     Document Type: Article
Times cited : (8)

References (20)
  • 2
    • 73549118380 scopus 로고    scopus 로고
    • The advances of the study on bioconversion to 1,3-propanediol
    • J. Wang, H. Liu and Z. Xiu, The advances of the study on bioconversion to 1,3-propanediol, Chemistry 64(10) (2001) 621-625.
    • (2001) Chemistry , vol.64 , Issue.10 , pp. 621-625
    • Wang, J.1    Liu, H.2    Xiu, Z.3
  • 3
    • 0029294162 scopus 로고
    • A kinetic model for product formation of microbial and mammalian cells
    • A. P. Zeng, A kinetic model for product formation of microbial and mammalian cells, Biotechnol. Bioeng. 46 (1995) 314-324.
    • (1995) Biotechnol. Bioeng. , vol.46 , pp. 314-324
    • Zeng, A.P.1
  • 4
    • 0028485952 scopus 로고
    • Multiple product inhibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in glycerol fermentation
    • A. P. Zeng, A. Rose, H. Biebl, C. Tag, B. Guenzel and W. D. Deckwer, Multiple product inhibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in glycerol fermentation, Biotechnol. Bioeng. 44 (1994) 902-911.
    • (1994) Biotechnol. Bioeng. , vol.44 , pp. 902-911
    • Zeng, A.P.1    Rose, A.2    Biebl, H.3    Tag, C.4    Guenzel, B.5    Deckwer, W.D.6
  • 5
    • 84984082112 scopus 로고
    • Dynamic behavior of the chemostat subject to substrate inhibition
    • T. Yano and S. Koga, Dynamic behavior of the chemostat subject to substrate inhibition, Biotechnol. Bioeng. 11 (1969) 139-153.
    • (1969) Biotechnol. Bioeng. , vol.11 , pp. 139-153
    • Yano, T.1    Koga, S.2
  • 6
    • 85008061027 scopus 로고
    • Dynamic behavior of the chemostat subject to product inhibition
    • T. Yano and S. Koga, Dynamic behavior of the chemostat subject to product inhibition, J. Gen. Appl. Microbiol. 19 (1973) 97-102.
    • (1973) J. Gen. Appl. Microbiol. , vol.19 , pp. 97-102
    • Yano, T.1    Koga, S.2
  • 7
    • 0030571578 scopus 로고    scopus 로고
    • Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture: I. The phenomena and characterization of oscillation and hysteresis
    • K. Menzel, A. P. Zeng, H. Biebl and W. D. Deckwer, Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture: I. The phenomena and characterization of oscillation and hysteresis, Biotechnol. Bioeng. 52 (1996) 549-560.
    • (1996) Biotechnol. Bioeng. , vol.52 , pp. 549-560
    • Menzel, K.1    Zeng, A.P.2    Biebl, H.3    Deckwer, W.D.4
  • 8
    • 0010006207 scopus 로고    scopus 로고
    • Mathematical modeling of kinetics and research on multiplicity of glycerol bioconversion to 1,3-propanediol
    • Z. L. Xiu, A. P. Zeng and L. J. An, Mathematical modeling of kinetics and research on multiplicity of glycerol bioconversion to 1,3-propanediol, J. Dalian Univ. Technol. 40 (2000) 428-433.
    • (2000) J. Dalian Univ. Technol. , vol.40 , pp. 428-433
    • Xiu, Z.L.1    Zeng, A.P.2    An, L.J.3
  • 9
    • 0032487108 scopus 로고    scopus 로고
    • Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture. III. Enzymes and fluxes of glycerol dissimilation and 1,3-propanediol formation
    • K. Ahrens, K. Menzel, A. P. Zeng and W. D. Deckwer, Kinetic, dynamic, and pathway studies of glycerol metabolism by Klebsiella pneumoniae in anaerobic continuous culture. III. Enzymes and fluxes of glycerol dissimilation and 1,3-propanediol formation, Biotechnol. Bioeng. 59(5) (1998) 544-552.
    • (1998) Biotechnol. Bioeng. , vol.59 , Issue.5 , pp. 544-552
    • Ahrens, K.1    Menzel, K.2    Zeng, A.P.3    Deckwer, W.D.4
  • 10
    • 0000258871 scopus 로고
    • Transient and oscillatory states of continuous culture
    • eds. T. K. Ghose, A. Fiechter, N. Blakesbrown (Springer, Berlin
    • D. E. F. Harrison and H. H. Topiwala, Transient and oscillatory states of continuous culture, in Advances in Biochemical Engineering/Biotechnology, eds. T. K. Ghose, A. Fiechter, N. Blakesbrown (Springer, Berlin, 1974), pp. 168-219.
    • (1974) Advances in Biochemical Engineering/Biotechnology , pp. 168-219
    • Harrison, D.E.F.1    Topiwala, H.H.2
  • 11
    • 0001189798 scopus 로고
    • Oscillation of filamentous bacterium Sphaerotilus spp. in continuous culture
    • N. Kurano, S. Kotera, M. Okazaki and Y. Miura, Oscillation of filamentous bacterium Sphaerotilus spp. in continuous culture, J. Ferment. Technol. 62(5) (1984) 395-400.
    • (1984) J. Ferment. Technol. , vol.62 , Issue.5 , pp. 395-400
    • Kurano, N.1    Kotera, S.2    Okazaki, M.3    Miura, Y.4
  • 12
    • 0031555010 scopus 로고    scopus 로고
    • Experimental investigation and modeling of oscillatory behavior in the continuous culture of Zymomonas mobilis
    • A. J. Daugulis, P. J. McLellan and J. Li, Experimental investigation and modeling of oscillatory behavior in the continuous culture of Zymomonas mobilis, Biotechnol. Bioeng. 56(1) (1997) 99-105.
    • (1997) Biotechnol. Bioeng. , vol.56 , Issue.1 , pp. 99-105
    • Daugulis, A.J.1    McLellan, P.J.2    Li, J.3
  • 13
    • 0032867719 scopus 로고    scopus 로고
    • The incidence of oscillatory behavior in the continuous fermentation of Zymomonas mobilis
    • P. J. McLellan, A. J. Daugulis and J. Li, The incidence of oscillatory behavior in the continuous fermentation of Zymomonas mobilis, Biotechnol. Prog. 15(4) (1999) 667-680.
    • (1999) Biotechnol. Prog. , vol.15 , Issue.4 , pp. 667-680
    • McLellan, P.J.1    Daugulis, A.J.2    Li, J.3
  • 14
    • 84863116818 scopus 로고    scopus 로고
    • An impulsive predator-prey system with Beddington-Deanelis functional response and time delay
    • H. Zhang, P. Georgescu and L. Chen, An impulsive predator-prey system with Beddington-Deanelis functional response and time delay, Int. J. Biomath. 57 (2008) 1-17.
    • (2008) Int. J. Biomath. , vol.57 , pp. 1-17
    • Zhang, H.1    Georgescu, P.2    Chen, L.3
  • 15
    • 84863116246 scopus 로고    scopus 로고
    • Globally dynamical behaviors for discrete Lasota-Wazewska model with several delays and almost periodic coefficients
    • X. Wang and Z. Li, Globally dynamical behaviors for discrete Lasota-Wazewska model with several delays and almost periodic coefficients, Int. J. Biomath. 57 (2008) 97-105.
    • (2008) Int. J. Biomath. , vol.57 , pp. 97-105
    • Wang, X.1    Li, Z.2
  • 16
    • 84863116297 scopus 로고    scopus 로고
    • Existence of positive periodic solutions for neutral population model with delays
    • Q. Wang and B. Dai, Existence of positive periodic solutions for neutral population model with delays, Int. J. Biomath. 57 (2008) 107-120.
    • (2008) Int. J. Biomath. , vol.57 , pp. 107-120
    • Wang, Q.1    Dai, B.2
  • 17
    • 84863161474 scopus 로고    scopus 로고
    • Stability of T -periodic solution on the extended simplified brusselator model
    • J. Lian and H. Zhang, Stability of T -periodic solution on the extended simplified brusselator model, Int. J. Biomath. 57 (2008) 19-27.
    • (2008) Int. J. Biomath. , vol.57 , pp. 19-27
    • Lian, J.1    Zhang, H.2
  • 18
    • 0032485059 scopus 로고    scopus 로고
    • Multiplicity and stability analysis of microorganisms in continuous culture: Effects of metabolic overflow and growth inhibition
    • Z. L. Xiu, A. P. Zeng and W. D. Deckwer, Multiplicity and stability analysis of microorganisms in continuous culture: Effects of metabolic overflow and growth inhibition, Biotechnol. Bioeng. 57 (1998) 251-261.
    • (1998) Biotechnol. Bioeng. , vol.57 , pp. 251-261
    • Xiu, Z.L.1    Zeng, A.P.2    Deckwer, W.D.3
  • 19
    • 71549146041 scopus 로고    scopus 로고
    • Stability and Hopf Bifurcation of a Differential Delay System
    • L. Li, Stability and Hopf Bifurcation of a Differential Delay System, J. Biomath. 17(2) (2002) 157-164.
    • (2002) J. Biomath. , vol.17 , Issue.2 , pp. 157-164
    • Li, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.