메뉴 건너뛰기




Volumn 7, Issue 4, 2007, Pages 779-792

Circular and elliptic orbits in a feedback-mediated chemostat

Author keywords

Chemostat; Conservative system; Feedback mediated control; Periodic coexistence

Indexed keywords


EID: 34250833831     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (1)

References (23)
  • 1
    • 33745131718 scopus 로고    scopus 로고
    • Consideration on yield, nutrient uptake, cellular growth, and competition in chemostat models
    • J. Arino, S.S. Pilyugin, and G.S.K. Wolkowicz, Consideration on yield, nutrient uptake, cellular growth, and competition in chemostat models, Can. Appl. Math. Quart., 11 (2003), 107-142.
    • (2003) Can. Appl. Math. Quart , vol.11 , pp. 107-142
    • Arino, J.1    Pilyugin, S.S.2    Wolkowicz, G.S.K.3
  • 2
    • 0022012911 scopus 로고
    • A Mathematical model of the chemostat with a general class of functions describing nutrient uptake
    • G.J. Butler and G.S.K. Wolkowicz, A Mathematical model of the chemostat with a general class of functions describing nutrient uptake, SIAM J. Appl. Math., 45 (1985), 138-151.
    • (1985) SIAM J. Appl. Math , vol.45 , pp. 138-151
    • Butler, G.J.1    Wolkowicz, G.S.K.2
  • 3
    • 0023306057 scopus 로고
    • Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources
    • G.J. Butler and G.S.K. Wolkowicz, Exploitative competition in a chemostat for two complementary, and possibly inhibitory, resources, Math. Biosci., 83 (1985), 1-48.
    • (1985) Math. Biosci , vol.83 , pp. 1-48
    • Butler, G.J.1    Wolkowicz, G.S.K.2
  • 4
    • 0022075298 scopus 로고
    • A mathematical model of a chemostat with periodic washout rate
    • G.J. Butler, S.B. Hsu, and P. Waltman, A mathematical model of a 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
  • 5
    • 0041758422 scopus 로고    scopus 로고
    • Feedback control for chemostat models
    • P. De Leenheer and H.L. Smith, Feedback control for chemostat models, J. Math. Biol., 46 (2003), 48-70.
    • (2003) J. Math. Biol , vol.46 , pp. 48-70
    • De Leenheer, P.1    Smith, H.L.2
  • 8
    • 15844396415 scopus 로고    scopus 로고
    • Feedback control for nonmonotone competition models in the chemostat
    • J.-L. Gouze and G. Robledo, Feedback control for nonmonotone competition models in the chemostat, Nonlinear Analysis: Real World Applications, 6 (2005), 671-690.
    • (2005) Nonlinear Analysis: Real World Applications , vol.6 , pp. 671-690
    • Gouze, J.-L.1    Robledo, G.2
  • 9
    • 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
  • 10
    • 0000468175 scopus 로고
    • Limiting behavior of competing species
    • S.-B. Hsu, Limiting behavior of competing species, SIAM J. Appl. Math., 34 (1978), 760-763.
    • (1978) SIAM J. Appl. Math , vol.34 , pp. 760-763
    • Hsu, S.-B.1
  • 11
    • 13444287117 scopus 로고
    • Limit cycles in a continuous fermentation model
    • X. Huang, Limit cycles in a continuous fermentation model, J. Math. Chem., 5 (1990), 287-296.
    • (1990) J. Math. Chem , vol.5 , pp. 287-296
    • Huang, X.1
  • 12
    • 25144493055 scopus 로고    scopus 로고
    • A three-dimensional chemostat with quadratic yields
    • X. Huang and L. Zhu, A three-dimensional chemostat with quadratic yields, J. Math. Chem., 38 (2005), 405-418.
    • (2005) J. Math. Chem , vol.38 , pp. 405-418
    • Huang, X.1    Zhu, L.2
  • 14
    • 49949129712 scopus 로고
    • Stability theory for ordinary differential equations
    • J. P. LaSalle, Stability theory for ordinary differential equations, J. Diff. Eqns., 4 (1968), 57-65.
    • (1968) J. Diff. Eqns , vol.4 , pp. 57-65
    • LaSalle, J.P.1
  • 15
    • 0016718782 scopus 로고
    • Competition between two species for complementary or substitutable substrates
    • J.A. Leon and D.B. Tumpson, Competition between two species for complementary or substitutable substrates, J. Theor. Biol., 50 (1975), 185-201.
    • (1975) J. Theor. Biol , vol.50 , pp. 185-201
    • Leon, J.A.1    Tumpson, D.B.2
  • 16
    • 0001555399 scopus 로고
    • Description of the chemostat
    • A. Novick and L. Szilard, Description of the chemostat, Science, 112 (1950), 715.
    • (1950) Science , vol.112 , pp. 715
    • Novick, A.1    Szilard, L.2
  • 17
    • 0037376825 scopus 로고    scopus 로고
    • Multiple limit cycles in the chemostat with variable yield
    • S.S. Pilyugin and P. Waltman, Multiple limit cycles in the chemostat with variable yield, Math. Biosci., 182 (2003), 151-166.
    • (2003) Math. Biosci , vol.182 , pp. 151-166
    • Pilyugin, S.S.1    Waltman, P.2
  • 18
    • 0025448723 scopus 로고
    • Controlled growth of competing species
    • N.S. Rao and E.O. Roxin, 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.O.2
  • 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), 498-522.
    • (1981) SIAM J. Appl. Math , vol.40 , pp. 498-522
    • Smith, H.L.1
  • 21
    • 0028483826 scopus 로고
    • Competition for a single limiting resource in continuous culture: The variable-yield model
    • H.L. Smith and P. Waltman, Competition for a single limiting resource in continuous culture: the variable-yield model, SIAM J. Appl. Math., 54 (1994), 1113-1131.
    • (1994) SIAM J. Appl. Math , vol.54 , pp. 1113-1131
    • Smith, H.L.1    Waltman, P.2
  • 22
    • 33646855094 scopus 로고    scopus 로고
    • Delayed feedback control for a chemostat model
    • O. Tagashira and T. Hara, Delayed feedback control for a chemostat model, Math. Biosci., 201 (2006), 101-112.
    • (2006) Math. Biosci , vol.201 , pp. 101-112
    • Tagashira, O.1    Hara, T.2
  • 23
    • 0009317097 scopus 로고    scopus 로고
    • N-Species competition in a periodic chemostat
    • G.S.K. Wolkowicz and X.-Q. Zhao, N-Species competition in a periodic chemostat, Diff. Int. Eqns., 11 (1998), 465-491.
    • (1998) Diff. Int. Eqns , vol.11 , pp. 465-491
    • Wolkowicz, G.S.K.1    Zhao, X.-Q.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.