메뉴 건너뛰기




Volumn 226, Issue 2, 2010, Pages 120-133

Ecological consequences of global bifurcations in some food chain models

Author keywords

Bistability; Food chain model; Global bifurcation; Separatrix disappearance; Shilni'kov bifurcation; Stoichiometry

Indexed keywords

BI-STABILITY; FOOD CHAIN MODEL; GLOBAL BIFURCATIONS; SEPARATRIX; SEPARATRIX DISAPPEARANCE;

EID: 77954144178     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2010.04.005     Document Type: Article
Times cited : (34)

References (43)
  • 7
    • 0043068053 scopus 로고    scopus 로고
    • Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment
    • Kooi B.W. Numerical bifurcation analysis of ecosystems in a spatially homogeneous environment. Acta Biotheor. 2003, 51:189.
    • (2003) Acta Biotheor. , vol.51 , pp. 189
    • Kooi, B.W.1
  • 8
    • 34047108600 scopus 로고    scopus 로고
    • Computation of equilibrium states and bifurcations using interval analysis: application to food chain models
    • Gwaltney C.R., Luo W., Stadtherr M.A. Computation of equilibrium states and bifurcations using interval analysis: application to food chain models. Ecol. Model. 2007, 203:495.
    • (2007) Ecol. Model. , vol.203 , pp. 495
    • Gwaltney, C.R.1    Luo, W.2    Stadtherr, M.A.3
  • 9
    • 60249100213 scopus 로고    scopus 로고
    • Joint effects of nutrients and contaminants on the dynamics of a food chain in marine ecosystems
    • Bacelar F.S., Dueri S., Hernández-García E., Zaldívar J.-M. Joint effects of nutrients and contaminants on the dynamics of a food chain in marine ecosystems. Math. Biosci. 2009, 218:24.
    • (2009) Math. Biosci. , vol.218 , pp. 24
    • Bacelar, F.S.1    Dueri, S.2    Hernández-García, E.3    Zaldívar, J.-M.4
  • 11
    • 0034680809 scopus 로고    scopus 로고
    • Crossing the Hopf bifurcation in a live predator-prey system
    • Fussman C.F., Ellner S.P., Shertzer K.W., Hairston N.G. Crossing the Hopf bifurcation in a live predator-prey system. Science 2000, 290:1358.
    • (2000) Science , vol.290 , pp. 1358
    • Fussman, C.F.1    Ellner, S.P.2    Shertzer, K.W.3    Hairston, N.G.4
  • 12
    • 21744442116 scopus 로고    scopus 로고
    • Experimental demonstration of chaos in a microbial food web
    • Becks L., Hilker F.M., Malchow H., Jürgens K., Arndt H. Experimental demonstration of chaos in a microbial food web. Nature 2005, 435:1226.
    • (2005) Nature , vol.435 , pp. 1226
    • Becks, L.1    Hilker, F.M.2    Malchow, H.3    Jürgens, K.4    Arndt, H.5
  • 14
    • 34548565990 scopus 로고    scopus 로고
    • Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect
    • van Voorn G.A.K., Hemerik L., Boer M.P., Kooi B.W. Heteroclinic orbits indicate overexploitation in predator-prey systems with a strong Allee effect. Math. Biosci. 2007, 209:451.
    • (2007) Math. Biosci. , vol.209 , pp. 451
    • van Voorn, G.A.K.1    Hemerik, L.2    Boer, M.P.3    Kooi, B.W.4
  • 16
    • 0001842302 scopus 로고    scopus 로고
    • Homoclinic and heteroclinic orbits to a cycle in a tri-trophic food chain
    • Boer M.P., Kooi B.W., Kooijman S.A.L.M. Homoclinic and heteroclinic orbits to a cycle in a tri-trophic food chain. J. Math. Biol. 1999, 39:19.
    • (1999) J. Math. Biol. , vol.39 , pp. 19
    • Boer, M.P.1    Kooi, B.W.2    Kooijman, S.A.L.M.3
  • 17
    • 0035109332 scopus 로고    scopus 로고
    • Multiple attractors and boundary crises in a tri-trophic food chain
    • Boer M.P., Kooi B.W., Kooijman S.A.L.M. Multiple attractors and boundary crises in a tri-trophic food chain. Math. Biosci. 2001, 169:109.
    • (2001) Math. Biosci. , vol.169 , pp. 109
    • Boer, M.P.1    Kooi, B.W.2    Kooijman, S.A.L.M.3
  • 19
    • 21844486228 scopus 로고
    • Numerical detection and continuation of codimension-two homoclinic bifurcations
    • Champneys A.R., Kuznetsov Yu.A. Numerical detection and continuation of codimension-two homoclinic bifurcations. Int. J. Bifurcation Chaos 1994, 4:785.
    • (1994) Int. J. Bifurcation Chaos , vol.4 , pp. 785
    • Champneys, A.R.1    Kuznetsov, Y.2
  • 21
    • 22244431913 scopus 로고    scopus 로고
    • Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem
    • Champneys A.R., Lord G.J. Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem. Physica D 1997, 102:101.
    • (1997) Physica D , vol.102 , pp. 101
    • Champneys, A.R.1    Lord, G.J.2
  • 23
    • 4043102017 scopus 로고    scopus 로고
    • Point-to-periodic and periodic-to-periodic connections
    • Dieci L., Rebaza R. Point-to-periodic and periodic-to-periodic connections. BIT Numer. Math. 2004, 44:41.
    • (2004) BIT Numer. Math. , vol.44 , pp. 41
    • Dieci, L.1    Rebaza, R.2
  • 24
    • 8144226661 scopus 로고    scopus 로고
    • Erratum: 'Point-to-periodic and periodic-to-periodic connections'
    • Dieci L., Rebaza R. Erratum: 'Point-to-periodic and periodic-to-periodic connections'. BIT Numer. Math. 2004, 44:617.
    • (2004) BIT Numer. Math. , vol.44 , pp. 617
    • Dieci, L.1    Rebaza, R.2
  • 26
    • 47849115552 scopus 로고    scopus 로고
    • A Lin's method approach to finding and continuing heteroclinic connections involving periodic orbits
    • Krauskopf B., Rieß T. A Lin's method approach to finding and continuing heteroclinic connections involving periodic orbits. Nonlinearity 2008, 21:1655.
    • (2008) Nonlinearity , vol.21 , pp. 1655
    • Krauskopf, B.1    Rieß, T.2
  • 27
    • 0033646273 scopus 로고    scopus 로고
    • Stoichiometry in producer-grazer systems: linking energy flow with element cycling
    • Loladze I., Kuang Y., Elser J.J. Stoichiometry in producer-grazer systems: linking energy flow with element cycling. Bull. Math. Biol. 2000, 62:1137.
    • (2000) Bull. Math. Biol. , vol.62 , pp. 1137
    • Loladze, I.1    Kuang, Y.2    Elser, J.J.3
  • 28
    • 0001524523 scopus 로고
    • Graphical representation and stability conditions of predator-prey interactions
    • Rosenzweig M.L., MacArthur R.H. Graphical representation and stability conditions of predator-prey interactions. Am. Nat. 1963, 97:209.
    • (1963) Am. Nat. , vol.97 , pp. 209
    • Rosenzweig, M.L.1    MacArthur, R.H.2
  • 29
    • 0036252851 scopus 로고    scopus 로고
    • Belyakov homoclinic bifurcations in a tri-trophic food chain model
    • Kuznetsov Yu.A., De Feo O., Rinaldi S. Belyakov homoclinic bifurcations in a tri-trophic food chain model. SIAM J. Appl. Math. 2001, 62:462.
    • (2001) SIAM J. Appl. Math. , vol.62 , pp. 462
    • Kuznetsov, Y.1    De Feo, O.2    Rinaldi, S.3
  • 30
    • 0036028189 scopus 로고    scopus 로고
    • Analysis of the dynamics of a realistic ecological model
    • Letellier C., Aziz-Alaoui M.A. Analysis of the dynamics of a realistic ecological model. Chaos Soliton Fract. 2002, 13:95.
    • (2002) Chaos Soliton Fract. , vol.13 , pp. 95
    • Letellier, C.1    Aziz-Alaoui, M.A.2
  • 31
    • 84880026161 scopus 로고
    • Some characteristics of simple types of predation and parasitism
    • Holling C.S. Some characteristics of simple types of predation and parasitism. Can. Entomol. 1959, 91:385.
    • (1959) Can. Entomol. , vol.91 , pp. 385
    • Holling, C.S.1
  • 32
    • 0015243940 scopus 로고
    • Paradox of enrichment: destabilization of exploitation ecosystems in ecological time
    • Rosenzweig M.L. Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 1971, 171:385.
    • (1971) Science , vol.171 , pp. 385
    • Rosenzweig, M.L.1
  • 33
    • 37049248026 scopus 로고
    • Enriched predator-prey systems: theoretical stability
    • Gilpin M.E. Enriched predator-prey systems: theoretical stability. Science 1972, 177:902.
    • (1972) Science , vol.177 , pp. 902
    • Gilpin, M.E.1
  • 36
    • 84951601313 scopus 로고
    • Chaos in three species food chains
    • Klebanoff A., Hastings A. Chaos in three species food chains. J. Math. Biol. 1994, 32:427.
    • (1994) J. Math. Biol. , vol.32 , pp. 427
    • Klebanoff, A.1    Hastings, A.2
  • 37
    • 0029663443 scopus 로고    scopus 로고
    • Remarks on food chain dynamics
    • Kuznetsov Yu.A., Rinaldi S. Remarks on food chain dynamics. Math. Biosci. 1996, 134:1.
    • (1996) Math. Biosci. , vol.134 , pp. 1
    • Kuznetsov, Y.1    Rinaldi, S.2
  • 38
    • 0012349493 scopus 로고
    • Crises, sudden changes in chaotic attractors, and transient chaos
    • Grebogi C., Ott E., Yorke J.A. Crises, sudden changes in chaotic attractors, and transient chaos. Physica D 1983, 7:181.
    • (1983) Physica D , vol.7 , pp. 181
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 40
    • 0042883694 scopus 로고    scopus 로고
    • Chaotic behaviour of a predator-prey system in the chemostat
    • Kooi B.W., Boer M.P. Chaotic behaviour of a predator-prey system in the chemostat. Dyn. Cont. Discr. Imp. Syst. 2003, 10:259.
    • (2003) Dyn. Cont. Discr. Imp. Syst. , vol.10 , pp. 259
    • Kooi, B.W.1    Boer, M.P.2
  • 41
    • 0028254194 scopus 로고
    • Nonlinear dynamics and population disappearances
    • McCann K., Yodzis P. Nonlinear dynamics and population disappearances. Am. Nat. 1994, 144:873.
    • (1994) Am. Nat. , vol.144 , pp. 873
    • McCann, K.1    Yodzis, P.2
  • 43
    • 36148980823 scopus 로고    scopus 로고
    • A new class of non-linear stochastic population models with mass conservation
    • Kooijman S.A.L.M., Grasman J., Kooi B.W. A new class of non-linear stochastic population models with mass conservation. Math. Biosci. 2007, 210:378.
    • (2007) Math. Biosci. , vol.210 , pp. 378
    • Kooijman, S.A.L.M.1    Grasman, J.2    Kooi, B.W.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.