메뉴 건너뛰기




Volumn 51, Issue 4, 2005, Pages 458-490

Global analysis of competition for perfectly substitutable resources with linear response

Author keywords

Bifurcation; Competition; Compound matrices; Lyapunov techniques; Perfectly substitutable resources

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; ECOSYSTEM; MATHEMATICS; STATISTICAL MODEL;

EID: 26444501613     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-005-0333-7     Document Type: Article
Times cited : (31)

References (39)
  • 1
    • 1042298863 scopus 로고    scopus 로고
    • Global results for an epidemic model with vaccination that exhibits backward bifurcation
    • Arino, J., McCluskey, C.C., van den Driessche, P.: Global results for an epidemic model with vaccination that exhibits backward bifurcation. SIAM J. Appl. Math. 64, 260-278 (2003)
    • (2003) SIAM J. Appl. Math. , vol.64 , pp. 260-278
    • Arino, J.1    McCluskey, C.C.2    Van Den Driessche, P.3
  • 2
    • 0001188059 scopus 로고
    • Competitive Exclusion
    • Armstrong, R.A., McGehee, R.: Competitive Exclusion. Am. Nat. 115, 151-170 (1980)
    • (1980) Am. Nat. , vol.115 , pp. 151-170
    • Armstrong, R.A.1    McGehee, R.2
  • 3
    • 0027329492 scopus 로고
    • Exploitative competition in the chemostat on two perfectly substitutable resources
    • Ballyk, M.M., Wolkowicz, G.S.K.: Exploitative competition in the chemostat on two perfectly substitutable resources. Math. Biosci. 118, 127-180 (1993)
    • (1993) Math. Biosci. , vol.118 , pp. 127-180
    • Ballyk, M.M.1    Wolkowicz, G.S.K.2
  • 4
    • 0001740271 scopus 로고
    • An examination of the thresholds of enrichment: A resource-based growth model
    • Ballyk, M.M., Wolkowicz, G.S.K.: An examination of the thresholds of enrichment: A resource-based growth model. J. Math. Biol. 33, 435-457 (1995)
    • (1995) J. Math. Biol. , vol.33 , pp. 435-457
    • Ballyk, M.M.1    Wolkowicz, G.S.K.2
  • 6
    • 0022012911 scopus 로고
    • A mathematical model of the chemostat with a general class of functions describing nutrient uptake
    • Butler, G.J., Wolkowicz, G.S.K.: A mathematical model of the chemostat with a general class of functions describing nutrient uptake. SIAM J. Appl. Math. 45, 138-151 (1985)
    • (1985) SIAM J. Appl. Math. , vol.45 , pp. 138-151
    • Butler, G.J.1    Wolkowicz, G.S.K.2
  • 7
    • 0023306057 scopus 로고
    • Exploitative competition in the chemostat for two complementary, and possibly inhibitory, resources
    • Butler, G.J., Wolkowicz, G.S.K.: Exploitative competition in the chemostat for two complementary, and possibly inhibitory, resources. Math. Biosci. 83, 1-48 (1987)
    • (1987) Math. Biosci. , vol.83 , pp. 1-48
    • Butler, G.J.1    Wolkowicz, G.S.K.2
  • 9
    • 18844400055 scopus 로고    scopus 로고
    • The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach
    • Diekmann, O., Jabin, P., Mischler, S., Perthame, B.: The dynamics of adaptation: An illuminating example and a Hamilton-Jacobi approach, Theoret. Pop. Biol. 67, 257-271 (2005)
    • (2005) Theoret. Pop. Biol. , vol.67 , pp. 257-271
    • Diekmann, O.1    Jabin, P.2    Mischler, S.3    Perthame, B.4
  • 11
    • 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, 213-231 (1984)
    • (1984) Math. Biosci. , vol.68 , pp. 213-231
    • Freedman, H.I.1    Waltman, P.2
  • 13
    • 0018868854 scopus 로고
    • Single nutrient microbial competition: Qualitative agreement between experimental and theoretically forecast results
    • Hansen, S.R.. Hubbell, S.P.: Single nutrient microbial competition: qualitative agreement between experimental and theoretically forecast results. Science 207, 1491-1493 (1980)
    • (1980) Science , vol.207 , pp. 1491-1493
    • Hansen, S.R.1    Hubbell, S.P.2
  • 14
    • 0000228768 scopus 로고
    • The continuous culture of bacteria: A theoretical and experimental study
    • Herbert, D., Elsworth, R., Telling, R.C.: The continuous culture of bacteria: a theoretical and experimental study. J. Gen. Microbiol. 4, 601-622 (1956)
    • (1956) J. Gen. Microbiol. , vol.4 , pp. 601-622
    • Herbert, D.1    Elsworth, R.2    Telling, R.C.3
  • 15
    • 0002366911 scopus 로고
    • The functional response of predators to prey density and its role in mimicry and population regulation
    • Holling, C.S.: The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomol. Soc. Canada 45, 3-60 (1965)
    • (1965) Mem. Entomol. Soc. Canada , vol.45 , pp. 3-60
    • Holling, C.S.1
  • 16
    • 0001010543 scopus 로고
    • Exploitative competition of microorganisms for two complementary nutrients in continuous culture
    • Hsu, S.B., Cheng, K.S., Hubbell, S.P.: Exploitative competition of microorganisms for two complementary nutrients in continuous culture. SIAM J. Appl. Math. 41, 422-444 (1981)
    • (1981) SIAM J. Appl. Math. , vol.41 , pp. 422-444
    • Hsu, S.B.1    Cheng, K.S.2    Hubbell, S.P.3
  • 17
    • 0000875842 scopus 로고
    • A mathematical theory of single nutrient competition in continuous cultures for microorganisms
    • Hsu, S.B., Hubbell, S.P., Waltman, P.: A mathematical theory of single nutrient competition in continuous cultures for microorganisms. SIAM J. Appl. Math. 32, 366-383 (1977)
    • (1977) SIAM J. Appl. Math. , vol.32 , pp. 366-383
    • Hsu, S.B.1    Hubbell, S.P.2    Waltman, P.3
  • 18
    • 0033604549 scopus 로고    scopus 로고
    • Biodiversity of plankton by species oscillations and chaos
    • Huisman, J., Weissing, F.J.: Biodiversity of plankton by species oscillations and chaos. Nature 402, 407-410 (1999)
    • (1999) Nature , vol.402 , pp. 407-410
    • Huisman, J.1    Weissing, F.J.2
  • 21
    • 0016718782 scopus 로고
    • Competition between two species for two complementary or substitutable resources
    • Léon, J.A., Tumpson, D.B.: Competition between two species for two complementary or substitutable resources. J. Theor. Biol. 50, 185-201 (1975)
    • (1975) J. Theor. Biol. , vol.50 , pp. 185-201
    • Léon, J.A.1    Tumpson, D.B.2
  • 22
    • 0036228880 scopus 로고    scopus 로고
    • How many species can two essential resources support?
    • Li, B., Smith, H.L.: How many species can two essential resources support? SIAM J. Appl. Math. 62, 336-366 (2001)
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 336-366
    • Li, B.1    Smith, H.L.2
  • 23
    • 0030544879 scopus 로고    scopus 로고
    • A geometric approach to global-stability problems
    • Li, M.Y., Muldowney, J.S.: A geometric approach to global-stability problems. SIAM J. Math. Anal. 27, 1070-1083 (1996)
    • (1996) SIAM J. Math. Anal. , vol.27 , pp. 1070-1083
    • Li, M.Y.1    Muldowney, J.S.2
  • 24
    • 0000147071 scopus 로고
    • On R.A. Smith's autonomous convergence theorem
    • Li, M.Y., Muldowney, J.S.: On R.A. Smith's autonomous convergence theorem. Rocky Mountain J. Math. 25, 365-379 (1995)
    • (1995) Rocky Mountain J. Math. , vol.25 , pp. 365-379
    • Li, M.Y.1    Muldowney, J.S.2
  • 27
    • 84880990802 scopus 로고
    • Compound matrices and ordinary differential equations
    • Muldowney, J.S.: Compound matrices and ordinary differential equations. Rocky Mountain J. Math. 20, 857-871 (1990)
    • (1990) Rocky Mountain J. Math. , vol.20 , pp. 857-871
    • Muldowney, J.S.1
  • 28
    • 0001555399 scopus 로고
    • Description of the chemostat
    • Novick, A., Sziliard, L.: Description of the chemostat. Science 112, 715-716 (1950)
    • (1950) Science , vol.112 , pp. 715-716
    • Novick, A.1    Sziliard, L.2
  • 29
    • 14544268128 scopus 로고    scopus 로고
    • Predicting stability of mixed cultures from single species experiments: 1. Phenomenological model
    • Pilyugin, S., Reeves, G.T., Narang, A.: Predicting stability of mixed cultures from single species experiments: 1. Phenomenological model. Math. Biosci. 192, 85-109 (2004)
    • (2004) Math. Biosci. , vol.192 , pp. 85-109
    • Pilyugin, S.1    Reeves, G.T.2    Narang, A.3
  • 30
    • 0001432625 scopus 로고
    • An optimization model of food selection
    • Rapport, D.J.: An optimization model of food selection. Am. Nat. 105, 575-587 (1971)
    • (1971) Am. Nat. , vol.105 , pp. 575-587
    • Rapport, D.J.1
  • 31
    • 0000419742 scopus 로고
    • The kinetics of functional response
    • Real, L.A.: The kinetics of functional response. Am. Nat. 111, 287-300 (1977)
    • (1977) Am. Nat. , vol.111 , pp. 287-300
    • Real, L.A.1
  • 32
    • 0000324665 scopus 로고
    • Partitioning of resources and the outcome of interspecific competition: A model and some general considerations
    • Stewart, F.M., Levin, B.R.: Partitioning of resources and the outcome of interspecific competition: A model and some general considerations. Am. Nat. 107, 171-198 (1973)
    • (1973) Am. Nat. , vol.107 , pp. 171-198
    • Stewart, F.M.1    Levin, B.R.2
  • 33
    • 0016632639 scopus 로고
    • Theoretical studies on the coexistence of competing species under continuous flow conditions
    • Taylor, P.A., Williams, P.H.LeB.: Theoretical studies on the coexistence of competing species under continuous flow conditions. Can. J. Microbiol. 21, 90-98 (1975)
    • (1975) Can. J. Microbiol. , vol.21 , pp. 90-98
    • Taylor, P.A.1    Williams, P.H.LeB.2
  • 34
    • 0000817765 scopus 로고
    • Resource competition between planktonic algae: An experimental and theoretical approach
    • Tilman, D.: Resource competition between planktonic algae: An experimental and theoretical approach. Ecology 58, 338-348 (1977)
    • (1977) Ecology , vol.58 , pp. 338-348
    • Tilman, D.1
  • 36
    • 0001119103 scopus 로고
    • Notice sur la loi que la population pursuit dans son accroissement. Correspond
    • Verhulst, P.F.: Notice sur la loi que la population pursuit dans son accroissement. Correspond. Math. Phys. 10, 113-121 (1938)
    • (1938) Math. Phys. , vol.10 , pp. 113-121
    • Verhulst, P.F.1
  • 37
    • 0001880021 scopus 로고
    • Variations and fluctuations of the number of individuals in animal species living together
    • Volterra, V.: Variations and fluctuations of the number of individuals in animal species living together. J. Conserv. (Conserv. Int. Explor. Mer) 3, 3-51 (1928)
    • (1928) J. Conserv. (Conserv. Int. Explor. Mer) , vol.3 , pp. 3-51
    • Volterra, V.1
  • 38
    • 85053514649 scopus 로고
    • Theoretical and experimental investigations of microbial competition in continuous culture
    • T. Burton, ed. Marcel Dekker, New York
    • Waltman, P., Hubbell, S.P., Hsu, S.B.: Theoretical and experimental investigations of microbial competition in continuous culture. In Modeling and Differential Equations, T. Burton, ed. Marcel Dekker, New York, 1980, pp. 107-152
    • (1980) Modeling and Differential Equations , pp. 107-152
    • Waltman, P.1    Hubbell, S.P.2    Hsu, S.B.3
  • 39
    • 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, 222-233 (1992)
    • (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.