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Volumn 25, Issue 1, 2005, Pages 11-23

Oscillations induced by the time lags in limited nutrient-consumer dynamic models

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BACTERIA; BIODIVERSITY; CHEMOSTATS; FUNCTIONS; LAKES; MATHEMATICAL MODELS; OSCILLATIONS; RECYCLING;

EID: 13544275551     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2004.10.010     Document Type: Article
Times cited : (4)

References (27)
  • 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., IMACS
    • 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 1989 J.C. Baltzer AG., Scientific Publishing Co., IMACS 175 181
    • (1989) Biomedical Modelling and Simulation , 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
    • 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 Equations Dyn Syst 2 1994 19 40
    • (1994) Diff Equations Dyn Syst , vol.2 , pp. 19-40
    • Beretta, E.1    Takeuchi, Y.2
  • 5
    • 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 Equations Dyn Syst 2 1994 263 288
    • (1994) Diff Equations Dyn Syst , vol.2 , pp. 263-288
    • Beretta, E.1    Takeuchi, Y.2
  • 6
    • 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
  • 7
    • 8744224750 scopus 로고    scopus 로고
    • Periodicity in delay equations by direct fixed point mapping
    • T.A. Burton, and B. Zhang Periodicity in delay equations by direct fixed point mapping Diff Equations Dyn Syst 6 1998 413 424
    • (1998) Diff Equations Dyn Syst , vol.6 , pp. 413-424
    • Burton, T.A.1    Zhang, B.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
    • 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
    • 0036489540 scopus 로고    scopus 로고
    • Asymptotic behaviour of the chemostat model with delayed response in growth
    • H.M. El-Owaidy, and M. Ismail Asymptotic behaviour of the chemostat model with delayed response in growth Chaos, Solitons & Fractals 13 2002 787 795
    • (2002) Chaos, Solitons & Fractals , vol.13 , pp. 787-795
    • El-Owaidy, H.M.1    Ismail, M.2
  • 11
    • 0001759394 scopus 로고
    • Competing predators for a prey in a chemostat model with periodic nutrient input
    • H.I. Freedman, and Feng Yang Competing predators for a prey in a chemostat model with periodic nutrient input J Math Biol 29 1991 715 732
    • (1991) J Math Biol , vol.29 , pp. 715-732
    • Freedman, H.I.1    Feng, Y.2
  • 12
    • 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
  • 13
    • 0343749071 scopus 로고
    • Chemostat competition with time delay
    • J. Eisenfeld D.S. Levine J.C. Baltzer AG., Scientific Publishing Co., IMACS
    • H.I. Freedman, J.W-H. So, and P. Waltman Chemostat competition with time delay J. Eisenfeld D.S. Levine Biomedical modelling and simulation 1989 J.C. Baltzer AG., Scientific Publishing Co., IMACS 171 173
    • (1989) Biomedical Modelling and Simulation , pp. 171-173
    • Freedman, H.I.1    So, J.W.-H.2    Waltman, P.3
  • 14
    • 0021071835 scopus 로고
    • Competition for fluctuating nutrient
    • J.K. Hale, and A.S. Somolinos Competition for fluctuating nutrient J Math Biol 18 1983 255 280
    • (1983) J Math Biol , vol.18 , pp. 255-280
    • Hale, J.K.1    Somolinos, A.S.2
  • 15
    • 0019152390 scopus 로고
    • A competition model for seasonally fluctuating nutrient
    • S.B. Hsu A competition model for seasonally fluctuating nutrient J Math Biol 9 1980 115 132
    • (1980) J Math Biol , vol.9 , pp. 115-132
    • Hsu, S.B.1
  • 16
    • 0000875842 scopus 로고
    • A mathematical theory for single nutrient competition in continuous cultures of micro organisms
    • S.B. Hsu, S. 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.2    Waltman, P.3
  • 17
    • 0020834234 scopus 로고
    • Oscillatory coexistence in the chemostat: A codimension two unfolding
    • J.P. Keener Oscillatory coexistence in the chemostat: a codimension two unfolding SIAM J Appl Math 43 1983 1005 1018
    • (1983) SIAM J Appl Math , vol.43 , pp. 1005-1018
    • Keener, J.P.1
  • 19
    • 0000513747 scopus 로고
    • Competitive coexistence in an oscillating chemostat
    • H.L. Smith Competitive coexistence in an oscillating chemostat SIAM J Appl Math 40 1981 498 512
    • (1981) SIAM J Appl Math , vol.40 , pp. 498-512
    • Smith, H.L.1
  • 21
    • 0041727671 scopus 로고    scopus 로고
    • Global stability of chemostat models involving time delays
    • V.S.H. Rao, and P.R.S. Rao Global stability of chemostat models involving time delays Diff Equations Dyn Syst 8 2000 1 28
    • (2000) Diff Equations Dyn Syst , vol.8 , pp. 1-28
    • Rao, V.S.H.1    Rao, P.R.S.2
  • 22
    • 4243189861 scopus 로고    scopus 로고
    • Global stability of chemostat models involving time delays and zones of no activation
    • V.S.H. Rao, and P.R.S. Rao Global stability of chemostat models involving time delays and zones of no activation Canadian Appl Math Quart 9 2001 273 300
    • (2001) Canadian Appl Math Quart , vol.9 , pp. 273-300
    • Rao, V.S.H.1    Rao, P.R.S.2
  • 23
    • 0041573457 scopus 로고    scopus 로고
    • Global stability in chemostat models involving time delays and wall growth
    • V.S.H. Rao, and P.R.S. Rao Global stability in chemostat models involving time delays and wall growth Nonlinear Anal Real World Appl 5 2004 141 158
    • (2004) Nonlinear Anal Real World Appl , vol.5 , pp. 141-158
    • Rao, V.S.H.1    Rao, P.R.S.2
  • 24
    • 4243085710 scopus 로고    scopus 로고
    • Mathematical models of microbial populations and issues concerning stability
    • V.S.H. Rao, and P.R.S. 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
    • Rao, V.S.H.1    Rao, P.R.S.2
  • 25
    • 1642312070 scopus 로고    scopus 로고
    • Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays
    • S. Yuan, M. Song, and M. Han Direction and stability of bifurcating periodic solutions of a chemostat model with two distributed delays Chaos, Solitons & Fractals 21 2004 1109 1123
    • (2004) Chaos, Solitons & Fractals , vol.21 , pp. 1109-1123
    • Yuan, S.1    Song, M.2    Han, M.3
  • 26
    • 0347355137 scopus 로고    scopus 로고
    • Bifurcation analysis of a chemostat model with two distributed delays
    • S. Yuan, and M. Han Bifurcation analysis of a chemostat model with two distributed delays Chaos, Solitons & Fractals 20 2004 995 1004
    • (2004) Chaos, Solitons & Fractals , vol.20 , pp. 995-1004
    • Yuan, S.1    Han, M.2
  • 27
    • 0037411677 scopus 로고    scopus 로고
    • Competition in the chemostat: Convergence of a model with delayed response in growth
    • S. Yuan, M. Han, and Ma Zhien Competition in the chemostat: convergence of a model with delayed response in growth Chaos, Solitons & Fractals 17 2003 659 667
    • (2003) Chaos, Solitons & Fractals , vol.17 , pp. 659-667
    • Yuan, S.1    Han, M.2    Zhien, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.