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Volumn 11, Issue 5, 2010, Pages 4476-4486

The effects of delayed growth response on the dynamic behaviors of the Monod type chemostat model with impulsive input nutrient concentration

Author keywords

Delay; Impulsive effect; Microorganism extinction; Monod type chemostat model; Permanence

Indexed keywords

DELAY; DISCRETE DYNAMICAL SYSTEMS; DYNAMIC BEHAVIORS; GROWTH RESPONSE; IMPULSIVE DIFFERENTIAL EQUATION; IMPULSIVE EFFECT; IMPULSIVE EFFECTS; NUTRIENT CONCENTRATIONS; PERIODIC SOLUTION; STROBOSCOPIC MAPS; SUFFICIENT CONDITIONS;

EID: 77955513189     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2010.05.030     Document Type: Article
Times cited : (24)

References (36)
  • 2
    • 0000875842 scopus 로고
    • A mathematical theory for single nutrient competition in continuous cultures of micro-organisms
    • S.B. Hsu, S.P. Hubbell, and P. Waltman A mathematical theory for single nutrient competition in continuous cultures of micro-organisms SIAM J. Appl. Math. 32 1977 366 383
    • (1977) SIAM J. Appl. Math. , vol.32 , pp. 366-383
    • Hsu, S.B.1    Hubbell, S.P.2    Waltman, P.3
  • 3
    • 0006080632 scopus 로고
    • Growth in a changing environment
    • A.M. Picket Growth in a changing environment M.J. Bazin, Microbial Population Dynamics 1982 CRC Press Florida 91 124
    • (1982) Microbial Population Dynamics , pp. 91-124
    • Picket, A.M.1
  • 4
    • 0000369563 scopus 로고
    • La technique de culture continue; Thorie et applications
    • J. Monod La technique de culture continue; thorie et applications Ann. Inst. Pasteur 79 1950 390 401
    • (1950) Ann. Inst. Pasteur , vol.79 , pp. 390-401
    • Monod, J.1
  • 5
    • 0018868854 scopus 로고
    • Single-nutrient microbial competition: Qualitative agreement between experimental and theoretically forecast outcomes
    • S.R. Hansen, and S.P. Hubbell Single-nutrient microbial competition: qualitative agreement between experimental and theoretically forecast outcomes Science 207 1980 1491 1493
    • (1980) Science , vol.207 , pp. 1491-1493
    • Hansen, S.R.1    Hubbell, S.P.2
  • 7
    • 84984087072 scopus 로고
    • Dynamics of microbial propagation: Models considering inhibitors and variable cell composition
    • D. Ramkrishna, A.G. Fredrickson, and H.M. Tsuchiya Dynamics of microbial propagation: models considering inhibitors and variable cell composition Biotechnol. Bioeng. 9 1967 129 170
    • (1967) Biotechnol. Bioeng. , vol.9 , pp. 129-170
    • Ramkrishna, D.1    Fredrickson, A.G.2    Tsuchiya, H.M.3
  • 8
    • 0017173061 scopus 로고
    • The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater
    • A.W. Bush, and A.E. Cook The effect of time delay and growth rate inhibition in the bacterial treatment of wastewater J. Theoret. Biol. 63 1976 385 395
    • (1976) J. Theoret. Biol. , vol.63 , pp. 385-395
    • Bush, A.W.1    Cook, A.E.2
  • 9
    • 0001453657 scopus 로고
    • Time lag in population growth response of isochrysis galbana to a variable nitrate environment
    • J. Caperon Time lag in population growth response of isochrysis galbana to a variable nitrate environment Ecology 50 1969 188 192
    • (1969) Ecology , vol.50 , pp. 188-192
    • Caperon, J.1
  • 10
    • 10644240707 scopus 로고    scopus 로고
    • Global stability of an SIR epidemicmodel with time delay
    • W. Ma, M. Song, and Y. Takeuchi Global stability of an SIR epidemicmodel with time delay Appl. Math. Lett. 17 2004 1141 1145
    • (2004) Appl. Math. Lett. , vol.17 , pp. 1141-1145
    • Ma, W.1    Song, M.2    Takeuchi, Y.3
  • 11
    • 33745211201 scopus 로고    scopus 로고
    • Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake
    • G. Fu, and W. Ma Hopf bifurcations of a variable yield chemostat model with inhibitory exponential substrate uptake Chaos Solitons Fractals 30 2006 845 850
    • (2006) Chaos Solitons Fractals , vol.30 , pp. 845-850
    • Fu, G.1    Ma, W.2
  • 12
    • 0030589755 scopus 로고    scopus 로고
    • Bifurcation analysis of a chemostat model with a distributed delay
    • S. Ruan, and G.S.K. Wolkowicz Bifurcation analysis of a chemostat model with a distributed delay J. Math. Anal. Appl. 204 1996 786 812
    • (1996) J. Math. Anal. Appl. , vol.204 , pp. 786-812
    • Ruan, S.1    Wolkowicz, G.S.K.2
  • 13
    • 0016299795 scopus 로고
    • Dynamics of chemostat culture: The effect of a delay in cell response
    • T.F. Thingstad, and T.I. Langeland Dynamics of chemostat culture: the effect of a delay in cell response J. Theoret. Biol. 48 1974 149 159
    • (1974) J. Theoret. Biol. , vol.48 , pp. 149-159
    • Thingstad, T.F.1    Langeland, T.I.2
  • 14
    • 0028419954 scopus 로고
    • Competition in the chemostat: Global asymptotic behavior of a model with delayed response in growth
    • S.F. Ellermeyer Competition in the chemostat: global asymptotic behavior of a model with delayed response in growth SIAM J. Appl. Math. 54 1994 456 465
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 456-465
    • Ellermeyer, S.F.1
  • 15
    • 0031208159 scopus 로고    scopus 로고
    • Global asymptotic behavior of a chemostat model with discrete delays
    • G.S.K. Wolkowicz, and H. Xia Global asymptotic behavior of a chemostat model with discrete delays SIAM J. Appl. Math. 57 1997 1019 1043
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1019-1043
    • Wolkowicz, G.S.K.1    Xia, H.2
  • 16
    • 0031258276 scopus 로고    scopus 로고
    • Competition in the chemostat: A distributed delay model and its global asymptotic behavior
    • PII S0036139995289842
    • G.S.K. Wolkowicz, H. Xia, and S. Ruan Competition in the chemostat: a distributed delay model and its global asymptotic behavior SIAM J. Appl. Math. 57 1997 1281 1310 (Pubitemid 127631484)
    • (1997) SIAM Journal on Applied Mathematics , vol.57 , Issue.5 , pp. 1281-1310
    • Wolkowicz, G.S.K.1    Xia, H.2    Ruan, S.3
  • 17
    • 18644364234 scopus 로고    scopus 로고
    • Transient oscillations induced by delayed growth response in the chemostat
    • H. Xia, G.S.K. Wolkowicz, and L. Wang Transient oscillations induced by delayed growth response in the chemostat J. Math. Biol. 50 2005 489 530
    • (2005) J. Math. Biol. , vol.50 , pp. 489-530
    • Xia, H.1    Wolkowicz, G.S.K.2    Wang, L.3
  • 18
    • 0011560396 scopus 로고
    • Global periodic solutions for a differential delay system modelling a microbial population in the chemostat
    • T. Zhao Global periodic solutions for a differential delay system modelling a microbial population in the chemostat J. Math. Anal. Appl. 193 1995 329 352
    • (1995) J. Math. Anal. Appl. , vol.193 , pp. 329-352
    • Zhao, T.1
  • 20
    • 0021071835 scopus 로고
    • Competition for fluctuating nutrient
    • J.K. Hale, and A.S. Somolinas Competition for fluctuating nutrient J. Math. Biol. 18 1983 255 280
    • (1983) J. Math. Biol. , vol.18 , pp. 255-280
    • Hale, J.K.1    Somolinas, A.S.2
  • 21
    • 0022075298 scopus 로고
    • A mathematical model of the chemostat with periodic washout rate
    • G.J. Buler, S.B. Hsu, and P. Waltman A mathematical model of the chemostat with periodic washout rate SIAM J. Appl. Math. 45 1985 435 449
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 435-449
    • Buler, G.J.1    Hsu, S.B.2    Waltman, P.3
  • 22
    • 0009317097 scopus 로고    scopus 로고
    • N-spicies competition in a periodic chemostat
    • G.S.K. Wolkowicz, and X.Q. Zhao N-spicies competition in a periodic chemostat Differ. Integral Equ. 11 1998 465 491
    • (1998) Differ. Integral Equ. , vol.11 , pp. 465-491
    • Wolkowicz, G.S.K.1    Zhao, X.Q.2
  • 25
    • 0037332898 scopus 로고    scopus 로고
    • Complex dynamics of Holling type II LotkaVolterra predatorprey system with impulsive perturbations on the predator
    • X. Liu, and L. Chen Complex dynamics of Holling type II LotkaVolterra predatorprey system with impulsive perturbations on the predator Chaos Solitons Fractals 16 2003 311 320
    • (2003) Chaos Solitons Fractals , vol.16 , pp. 311-320
    • Liu, X.1    Chen, L.2
  • 26
    • 10244240509 scopus 로고    scopus 로고
    • The dynamical behaviors of a LotkaVolterra predatorprey model concerning integrated pest management
    • B. Liu, Y. Zhang, and L. Chen The dynamical behaviors of a LotkaVolterra predatorprey model concerning integrated pest management Nonlinear Anal. RWA 6 2005 227 243
    • (2005) Nonlinear Anal. RWA , vol.6 , pp. 227-243
    • Liu, B.1    Zhang, Y.2    Chen, L.3
  • 27
    • 0031468520 scopus 로고    scopus 로고
    • Permanence of population growth models with impulsive effects
    • G. Ballinger, and X. Liu Permanence of population growth models with impulsive effects Math. Comput. Modelling 26 1997 59 72
    • (1997) Math. Comput. Modelling , vol.26 , pp. 59-72
    • Ballinger, G.1    Liu, X.2
  • 28
    • 52049087331 scopus 로고    scopus 로고
    • Dynamics of a predatorprey system with pulses
    • Y. Li, J. Cui, and X. Song Dynamics of a predatorprey system with pulses Appl. Math. Comput. 204 2008 269 280
    • (2008) Appl. Math. Comput. , vol.204 , pp. 269-280
    • Li, Y.1    Cui, J.2    Song, X.3
  • 29
    • 84863116818 scopus 로고    scopus 로고
    • An impulsive predatorprey system with BeddingtonDeangelis functional response and time delay
    • H. Zhang, P. Georgescu, and L. Chen An impulsive predatorprey system with BeddingtonDeangelis functional response and time delay Int. J. Biomath. 1 2008 1 17
    • (2008) Int. J. Biomath. , vol.1 , pp. 1-17
    • Zhang, H.1    Georgescu, P.2    Chen, L.3
  • 30
    • 0027706230 scopus 로고
    • Invasion and chaos in a periodically pulsed mass-action chemostat
    • E. Funasaki, and M. Kot Invasion and chaos in a periodically pulsed mass-action chemostat Theor. Popul. Biol. 44 1993 203 224
    • (1993) Theor. Popul. Biol. , vol.44 , pp. 203-224
    • Funasaki, E.1    Kot, M.2
  • 31
    • 4544232712 scopus 로고    scopus 로고
    • Analysis of a model of the nutrient driven self-cycling fermentation process
    • R.J. Smith, and G.S.K. Wolkowicz Analysis of a model of the nutrient driven self-cycling fermentation process Dyn. Contin. Discrete Impul. Syst. Ser. B 11 2004 239 265
    • (2004) Dyn. Contin. Discrete Impul. Syst. Ser. B , vol.11 , pp. 239-265
    • Smith, R.J.1    Wolkowicz, G.S.K.2
  • 32
    • 38149117106 scopus 로고    scopus 로고
    • Dynamic behaviors of Monod type chemostat model with impulsive perturbation on the nutrient concentration
    • S. Sun, and L. Chen Dynamic behaviors of Monod type chemostat model with impulsive perturbation on the nutrient concentration J. Math. Chemistry 42 2007 837 847
    • (2007) J. Math. Chemistry , vol.42 , pp. 837-847
    • Sun, S.1    Chen, L.2
  • 33
    • 37248999845 scopus 로고    scopus 로고
    • The dynamics of an age structured predatorCprey model with disturbing pulse and time delays
    • X. Meng, J. Jiao, and L. Chen The dynamics of an age structured predatorCprey model with disturbing pulse and time delays Nonlinear Anal. RWA 9 2008 547 561
    • (2008) Nonlinear Anal. RWA , vol.9 , pp. 547-561
    • Meng, X.1    Jiao, J.2    Chen, L.3
  • 34
    • 44649122225 scopus 로고    scopus 로고
    • The effects of pulse vaccination on SEIR model with two time delays
    • S. Gao, Z. Teng, and D. Xie The effects of pulse vaccination on SEIR model with two time delays Appl. Math. Comput. 201 2008 282 292
    • (2008) Appl. Math. Comput. , vol.201 , pp. 282-292
    • Gao, S.1    Teng, Z.2    Xie, D.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.