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Volumn 171, Issue 1, 2001, Pages 132-147

Persistence criteria for a chemostat with variable nutrient input

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EID: 0035917056     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.4041     Document Type: Article
Times cited : (29)

References (24)
  • 1
    • 0032188337 scopus 로고    scopus 로고
    • Necessary and sufficient average growth in a Lotka-Volterra system
    • Ahmad Sh., Lazer A. C. Necessary and sufficient average growth in a Lotka-Volterra system. Nonlinear Anal. 34:1998.
    • (1998) Nonlinear Anal. , vol.34
    • Ahmad, Sh.1    Lazer A., C.2
  • 2
    • 0022075298 scopus 로고
    • A mathematical model of the chemostat with periodic washout rate
    • Butler G. J., Hsu S. B., Waltman P. 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
  • 4
    • 84966258595 scopus 로고
    • Persistence definitions and their connections
    • Freedman H. I., Moson P. Persistence definitions and their connections. Proc. Amer. Math. Soc. 109:1990;1025-1033.
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 1025-1033
    • Freedman H., I.1    Moson, P.2
  • 5
    • 48749138514 scopus 로고
    • Persistence in models of three interacting predator-prey populations
    • Freedman H. I., Waltman P. Persistence in models of three interacting predator-prey populations. Math. Biosci. 68:1984;213-231.
    • (1984) Math. Biosci. , vol.68 , pp. 213-231
    • Freedman H., I.1    Waltman, P.2
  • 6
    • 0002676883 scopus 로고
    • Persistence in a model of three competitive populations
    • Freedman H. I., Waltman P. Persistence in a model of three competitive populations. Math. Biosci. 73:1985;89-101.
    • (1985) Math. Biosci. , vol.73 , pp. 89-101
    • Freedman H., I.1    Waltman, P.2
  • 7
    • 0021071835 scopus 로고
    • Competition for fluctuating nutrient
    • Hale J. K., Somolinos A. S. 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
  • 8
    • 0022918323 scopus 로고
    • Persistence in population models with demographic fluctuations
    • Hallam T. G., Ma Z. Persistence in population models with demographic fluctuations. J. Math. Biol. 24:1986;327-339.
    • (1986) J. Math. Biol. , vol.24 , pp. 327-339
    • Hallam T., G.1    Ma, Z.2
  • 9
    • 0018868854 scopus 로고
    • Single nutrient microbial competition: Agreement between experimental and theoretical forecast outcomes
    • Hansen S. R., Hubbell S. P. Single nutrient microbial competition: Agreement between experimental and theoretical forecast outcomes. Science. 207:1980;1491-1493.
    • (1980) Science , vol.207 , pp. 1491-1493
    • Hansen S., R.1    Hubbell S., P.2
  • 11
    • 0019152390 scopus 로고
    • A competition model for a seasonally fluctuating nutrient
    • Hsu S. B. A competition model for a seasonally fluctuating nutrient. J. Math. Biol. 9:1980;115-132.
    • (1980) J. Math. Biol. , vol.9 , pp. 115-132
    • Hsu S., B.1
  • 12
    • 0000468175 scopus 로고
    • Limiting behavior for competing species
    • Hsu S. B. Limiting behavior for competing species. SIAM J. Appl. Math. 134:1978;760-763.
    • (1978) SIAM J. Appl. Math. , vol.134 , pp. 760-763
    • Hsu S., B.1
  • 13
    • 0026616222 scopus 로고
    • Permanence and the dynamics of biological systems
    • Hutson V., Schmitt K. Permanence and the dynamics of biological systems. Math. Biosci. 111:1992;1-74.
    • (1992) Math. Biosci. , vol.111 , pp. 1-74
    • Hutson, V.1    Schmitt, K.2
  • 14
    • 0032436718 scopus 로고    scopus 로고
    • Shaken not stirred: On permanence in ecological communities
    • Jansen V. A. A., Sigmund K. Shaken not stirred: On permanence in ecological communities. Theoret. Popul. Biol. 54:1998;195-201.
    • (1998) Theoret. Popul. Biol. , vol.54 , pp. 195-201
    • Jansen V. A., A.1    Sigmund, K.2
  • 16
    • 0025448723 scopus 로고
    • Controlled growth of competing species
    • Rao N. S., Roxin E. R. Controlled growth of competing species. SIAM J. Appl. Math. 50:1990;853-864.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 853-864
    • Rao N., S.1    Roxin E., R.2
  • 17
    • 0007016716 scopus 로고
    • A note on the Littlewood three-derivates theorem
    • Redheffer R. A note on the Littlewood three-derivates theorem. J. Lond. Math. Soc. 9:1974;9-15.
    • (1974) J. Lond. Math. Soc. , vol.9 , pp. 9-15
    • Redheffer, R.1
  • 18
    • 85031483093 scopus 로고    scopus 로고
    • Lotka-Volterra systems with constant interaction coefficients
    • to appear
    • R. Redheffer, Lotka-Volterra systems with constant interaction coefficients, Nonlinear Anal, to appear.
    • Nonlinear Anal
    • Redheffer, R.1
  • 19
    • 0000513747 scopus 로고
    • Competitive coexistence in an oscillating chemostat
    • Smith H. L. Competitive coexistence in an oscillating chemostat. SIAM J. Appl. Math. 40:1981;498-522.
    • (1981) SIAM J. Appl. Math. , vol.40 , pp. 498-522
    • Smith H., L.1
  • 21
    • 0018519318 scopus 로고
    • The growth of competing microbial populations in a CSTR with periodically varying inputs
    • Stephanopoulos G., Frederickson A. G., Aris R. The growth of competing microbial populations in a CSTR with periodically varying inputs. AIChE J. 25:1979;863-872.
    • (1979) AIChE J. , vol.25 , pp. 863-872
    • Stephanopoulos, G.1    Frederickson A., G.2    Aris, R.3
  • 22
    • 0039591930 scopus 로고
    • Persistence under relaxed point-dissapitivity (with application to an endemic model)
    • Thieme H. R. Persistence under relaxed point-dissapitivity (with application to an endemic model). SIAM J. Math. Anal. 24:1993;407-435.
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 407-435
    • Thieme H., R.1
  • 24
    • 0026818163 scopus 로고
    • Global dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates
    • Wolkowicz G. S. K., Lu Z. Global dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates. SIAM J. Appl. Math. 52:1992;222-233.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 222-233
    • Wolkowicz G. S., K.1    Lu, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.