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Volumn 28, Issue 5, 2006, Pages 1222-1251

Mathematical models and stabilizing bio-control mechanisms for microbial populations in a cultured environment

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; MATERIALS SCIENCE; MATHEMATICAL MODELS; RECYCLING;

EID: 29144536787     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.07.015     Document Type: Article
Times cited : (8)

References (40)
  • 1
    • 0005799132 scopus 로고
    • Stability and Hopf bifurcations in some nutrient-species models with nutrient recycling and time lags
    • J. Eisenfeld D.S. Levine J.C. Baltzer AG., Scientific Publishing Co.
    • E. Beretta, and G.I. Bischi Stability and Hopf bifurcations in some nutrient-species models with nutrient recycling and time lags J. Eisenfeld D.S. Levine Biomedical modelling and simulation. IMACS 1989 J.C. Baltzer AG., Scientific Publishing Co. 175 181
    • (1989) Biomedical Modelling and Simulation. IMACS , pp. 175-181
    • Beretta, E.1    Bischi, G.I.2
  • 2
    • 0011561462 scopus 로고
    • Oscillations in a system with material recycling
    • E. Beretta, G.I. Bischi, and F. Solimano Oscillations in a system with material recycling J Math Biol 26 1988 143 167
    • (1988) J Math Biol , vol.26 , pp. 143-167
    • Beretta, E.1    Bischi, G.I.2    Solimano, F.3
  • 3
    • 0025152436 scopus 로고
    • Stability in chemostat models with delayed nutrient recycling
    • E. Beretta, G.I. Bischi, and F. Solimano Stability in chemostat models with delayed nutrient recycling J Math Biol 28 1990 99 111
    • (1990) J Math Biol , vol.28 , pp. 99-111
    • Beretta, E.1    Bischi, G.I.2    Solimano, F.3
  • 4
    • 4243172002 scopus 로고    scopus 로고
    • Global stability in a well known delayed chemostat model
    • E. Beretta, and Y. Kuang Global stability in a well known delayed chemostat model Commun Appl Anal 4 2000 147 155
    • (2000) Commun Appl Anal , vol.4 , pp. 147-155
    • Beretta, E.1    Kuang, Y.2
  • 5
    • 0001864149 scopus 로고
    • Qualitative properties of chemostat equations with time delays, Boundedness, local and global asymptotic stability
    • E. Beretta, and Y. Takeuchi Qualitative properties of chemostat equations with time delays, Boundedness, local and global asymptotic stability Diff Equat Dyn Syst 2 1994 19 40
    • (1994) Diff Equat Dyn Syst , vol.2 , pp. 19-40
    • Beretta, E.1    Takeuchi, Y.2
  • 6
    • 0000128494 scopus 로고
    • Qualitative properties of chemostat equations with time delays
    • E. Beretta, and Y. Takeuchi Qualitative properties of chemostat equations with time delays Diff Equat Dyn Syst 2 1994 263 288
    • (1994) Diff Equat Dyn Syst , vol.2 , pp. 263-288
    • Beretta, E.1    Takeuchi, Y.2
  • 7
    • 0011678840 scopus 로고
    • Global stability for chemostat equations with delayed nutrient recycling
    • E. Beretta, and Y. Takeuchi Global stability for chemostat equations with delayed nutrient recycling Nonlin World 1 1994 291 306
    • (1994) Nonlin World , vol.1 , pp. 291-306
    • Beretta, E.1    Takeuchi, Y.2
  • 8
    • 0022075298 scopus 로고
    • A mathematical model of the chemostat with periodic washout rate
    • G.J. Butler, 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
    • Butler, G.J.1    Hsu, S.B.2    Waltman, P.3
  • 9
    • 0017173061 scopus 로고
    • The effect of time delay and growth rate inhibition in the bacterial decomposition of waste water
    • A.W. Bush, and A.E. Cook The effect of time delay and growth rate inhibition in the bacterial decomposition of waste water J Theor Biol 63 1975 385 395
    • (1975) J Theor Biol , vol.63 , pp. 385-395
    • Bush, A.W.1    Cook, A.E.2
  • 10
    • 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
  • 11
    • 0015314276 scopus 로고
    • A simulation study of a time lag population model
    • H. Caswell A simulation study of a time lag population model J Theor Biol 34 1972 419 439
    • (1972) J Theor Biol , vol.34 , pp. 419-439
    • Caswell, H.1
  • 14
    • 84974098072 scopus 로고
    • 12 and Marine ecology III. An experiment with a chemostat
    • 12 and Marine ecology III. An experiment with a chemostat J Mar Biol Ass UK 46 1966 659 671
    • (1966) J Mar Biol Ass UK , vol.46 , pp. 659-671
    • Droop, M.R.1
  • 15
    • 0028419954 scopus 로고
    • Competition in the chemostat: Global asymptotic behaviour of a model with delayed response in growth
    • S.F. Ellermeyer Competition in the chemostat: global asymptotic behaviour 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
  • 16
    • 4243131070 scopus 로고    scopus 로고
    • On the dynamics of a chemostat model with delayed nutrient recycling
    • P. Fergola, L. Jiang, and Z. Ma On the dynamics of a chemostat model with delayed nutrient recycling Intl J Appl Math Comput Sci 10 2000 81 96
    • (2000) Intl J Appl Math Comput Sci , vol.10 , pp. 81-96
    • Fergola, P.1    Jiang, L.2    Ma, Z.3
  • 17
    • 0001503284 scopus 로고
    • Coexistence in a model of competition in the chemostat incorporating discrete delays
    • H.I. Freedman, J.W.-H. So, and P. Waltman Coexistence in a model of competition in the chemostat incorporating discrete delays SIAM J Appl Math 49 1989 859 870
    • (1989) SIAM J Appl Math , vol.49 , pp. 859-870
    • Freedman, H.I.1    So, J.W.-H.2    Waltman, P.3
  • 18
    • 0343749071 scopus 로고
    • Chemostat competition with time delays
    • J. Eisenfeld D.S. Levine J.C. Baltzer AG., Scientific Publishing Co.
    • H.I. Freedman, J.W.-H. So, and P. Waltman Chemostat competition with time delays J. Eisenfeld D.S. Levine Biomedical modelling and simulation. IMACS 1989 J.C. Baltzer AG., Scientific Publishing Co. 171 173
    • (1989) Biomedical Modelling and Simulation. IMACS , pp. 171-173
    • Freedman, H.I.1    So, J.W.-H.2    Waltman, P.3
  • 19
    • 0001352326 scopus 로고
    • The trade-off between mutual interference and time lags in predator-prey systems
    • H.I. Freedman, and V. Sree Hari Rao The trade-off between mutual interference and time lags in predator-prey systems Bull Math Biol 45 1983 991 1004
    • (1983) Bull Math Biol , vol.45 , pp. 991-1004
    • Freedman, H.I.1    Sree Hari Rao, V.2
  • 20
    • 0002797068 scopus 로고
    • Models of competition in the chemostat with instantaneous and delayed nutrient recycling
    • H.I. Freedman, and Y. Xu Models of competition in the chemostat with instantaneous and delayed nutrient recycling J Math Biol 31 1993 513 527
    • (1993) J Math Biol , vol.31 , pp. 513-527
    • Freedman, H.I.1    Xu, Y.2
  • 22
    • 0006674647 scopus 로고    scopus 로고
    • Global stability in chemostat-type plankton models with delayed nutrient recycling
    • X.Z. He, and S. Ruan Global stability in chemostat-type plankton models with delayed nutrient recycling J Math Biol 37 1998 253 271
    • (1998) J Math Biol , vol.37 , pp. 253-271
    • He, X.Z.1    Ruan, S.2
  • 23
    • 0031997297 scopus 로고    scopus 로고
    • Global stability in chemostat-type competition models with nutrient recycling
    • X.Z. He, and S. Ruan Global stability in chemostat-type competition models with nutrient recycling SIAM J Appl Math 58 1998 170 192
    • (1998) SIAM J Appl Math , vol.58 , pp. 170-192
    • He, X.Z.1    Ruan, S.2
  • 24
    • 0032399698 scopus 로고    scopus 로고
    • Global stability in chemostat-type equations with distributed time delays
    • X. He, S. Ruan, and H. Xia Global stability in chemostat-type equations with distributed time delays SIAM J Math Anal 29 1998 681 696
    • (1998) SIAM J Math Anal , vol.29 , pp. 681-696
    • He, X.1    Ruan, S.2    Xia, H.3
  • 28
    • 0020748045 scopus 로고
    • A strategic model of material recycling in a closed ecosystem
    • R.M. Nisbet, J. Mckinstry, and W.S.C. Gurney A strategic model of material recycling in a closed ecosystem Math Biosci 64 1983 99 113
    • (1983) Math Biosci , vol.64 , pp. 99-113
    • Nisbet, R.M.1    McKinstry, J.2    Gurney, W.S.C.3
  • 29
    • 0033349132 scopus 로고    scopus 로고
    • The simple chemostat with wall growth
    • S.S. Pilyugin, and P. Waltman The simple chemostat with wall growth SIAM J Appl Math 59 1999 1552 1572
    • (1999) SIAM J Appl Math , vol.59 , pp. 1552-1572
    • Pilyugin, S.S.1    Waltman, P.2
  • 30
    • 0000778770 scopus 로고
    • The effect of time delays on stability and persistence in plankton models
    • S. Ruan The effect of time delays on stability and persistence in plankton models Nonlin Anal Theory Meth Appl 24 1995 575 585
    • (1995) Nonlin Anal Theory Meth Appl , vol.24 , pp. 575-585
    • Ruan, S.1
  • 32
    • 0041727671 scopus 로고    scopus 로고
    • Global stability of chemostat models involving time delays
    • V. Sree Hari Rao, and P. Raja Sekhara Rao Global stability of chemostat models involving time delays Diff Equat Dyn Syst 8 2000 1 28
    • (2000) Diff Equat Dyn Syst , vol.8 , pp. 1-28
    • Sree Hari Rao, V.1    Raja Sekhara Rao, P.2
  • 34
    • 4243189861 scopus 로고    scopus 로고
    • Global stability in chemostat models involving time delays and zones of no activation
    • V. Sree Hari Rao, and P. Raja Sekhara Rao Global stability in chemostat models involving time delays and zones of no activation Canad Appl Math Quart 9 2001 273 300
    • (2001) Canad Appl Math Quart , vol.9 , pp. 273-300
    • Sree Hari Rao, V.1    Raja Sekhara Rao, P.2
  • 35
    • 0041573457 scopus 로고    scopus 로고
    • Global stability in chemostat models involving time delays and wall growth
    • V. Sree Hari Rao, and P. Raja Sekhara Rao Global stability in chemostat models involving time delays and wall growth Nonlin Analy-Real World Appl 5 2004 141 158
    • (2004) Nonlin Analy-Real World Appl , vol.5 , pp. 141-158
    • Sree Hari Rao, V.1    Raja Sekhara Rao, P.2
  • 36
    • 4243085710 scopus 로고    scopus 로고
    • Mathematical models of microbial populations and issues concerning stability
    • V. Sree Hari Rao, and P. Raja Sekhara Rao Mathematical models of microbial populations and issues concerning stability Chaos, Solitons & Fractals 23 2005 657 670
    • (2005) Chaos, Solitons & Fractals , vol.23 , pp. 657-670
    • Sree Hari Rao, V.1    Raja Sekhara Rao, P.2
  • 37
    • 13544275551 scopus 로고    scopus 로고
    • Oscillations induced by the time lags in limited nutrient-consumer dynamic models
    • V. Sree Hari Rao, and P. Raja Sekhara Rao Oscillations induced by the time lags in limited nutrient-consumer dynamic models Chaos, Solitons & Fractals 25 2005 11 23
    • (2005) Chaos, Solitons & Fractals , vol.25 , pp. 11-23
    • Sree Hari Rao, V.1    Raja Sekhara Rao, P.2
  • 39
    • 3042525371 scopus 로고
    • Co-existence in chemostat-like models
    • P. Waltman Co-existence in chemostat-like models Rocky Mountain J Math 20 1990 777 807
    • (1990) Rocky Mountain J Math , vol.20 , pp. 777-807
    • Waltman, P.1
  • 40
    • 0000640281 scopus 로고
    • Theoretical and experimental investigations of microbial competition in continuous culture
    • T.A. Burton Marcel Dekker NY
    • P. Waltman, S.P. Hubbell, and S.B. Hsu Theoretical and experimental investigations of microbial competition in continuous culture T.A. Burton Modeling and differential equations in biology 1980 Marcel Dekker NY
    • (1980) Modeling and Differential Equations in Biology
    • Waltman, P.1    Hubbell, S.P.2    Hsu, S.B.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.