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Volumn 43, Issue 3, 2001, Pages 221-246

Parametric analysis of the ratio-dependent predator-prey model

Author keywords

Bifurcation; Biological control; Complicated singular point; Dynamical system; Phase portrait; Population dynamics

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ECOLOGY; POPULATION DYNAMICS; PREDATION;

EID: 0035460669     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850000078     Document Type: Article
Times cited : (173)

References (40)
  • 1
    • 0027954761 scopus 로고
    • The fallacies of "ratio-dependent" predation
    • Abrams, P.A.: The fallacies of "ratio-dependent" predation. Ecology, 75, 1842-1850 (1994)
    • (1994) Ecology , vol.75 , pp. 1842-1850
    • Abrams, P.A.1
  • 2
    • 0034255819 scopus 로고    scopus 로고
    • The nature of predation: Prey dependent, ratio dependent or neither?
    • Abrams, P.A., Ginzburg, L.R.: The nature of predation: prey dependent, ratio dependent or neither? Trends Ecol. Evol., 15, 337-341 (2000)
    • (2000) Trends Ecol. Evol. , vol.15 , pp. 337-341
    • Abrams, P.A.1    Ginzburg, L.R.2
  • 3
    • 0028974970 scopus 로고
    • Ratio-dependent predation: An abstraction that works
    • Akçakaya, H.R., Arditi, R., Ginzburg, L.R.: Ratio-dependent predation: an abstraction that works, Ecology, 76, 995-1004 (1995)
    • (1995) Ecology , vol.76 , pp. 995-1004
    • Akçakaya, H.R.1    Arditi, R.2    Ginzburg, L.R.3
  • 5
    • 4944258042 scopus 로고
    • Coupling in predator-prey dynamics: Ratio-dependence
    • Arditi, R., Ginzburg, L.R.: Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol., 139, 311-326 (1989)
    • (1989) J. Theor. Biol. , vol.139 , pp. 311-326
    • Arditi, R.1    Ginzburg, L.R.2
  • 6
    • 0000542895 scopus 로고
    • Variation in plankton densities among lakes: A case for ratio-dependent predation models
    • Arditi, R., Ginzburg, L.R., Akçakaya, H.R.: Variation in plankton densities among lakes: a case for ratio-dependent predation models. Am. Nat., 138, 1287-1296 (1991)
    • (1991) Am. Nat. , vol.138 , pp. 1287-1296
    • Arditi, R.1    Ginzburg, L.R.2    Akçakaya, H.R.3
  • 7
    • 0001505203 scopus 로고
    • Scale invariance is a reasonable approximation in predation models - Reply to Ruxton and Gurney
    • Arditi, R., Ginzburg, L.R., Perrin, N.: Scale invariance is a reasonable approximation in predation models - reply to Ruxton and Gurney. Oikos, 65, 336-337 (1992)
    • (1992) Oikos , vol.65 , pp. 336-337
    • Arditi, R.1    Ginzburg, L.R.2    Perrin, N.3
  • 8
    • 0002664347 scopus 로고    scopus 로고
    • Nonlinear food web models and their responses to increased basal productivity
    • Polis, G.A., Winemiller, K.O. (eds) Chapman and Hall, New York
    • Arditi, R., Michalski, J.: Nonlinear food web models and their responses to increased basal productivity. In: Polis, G.A., Winemiller, K.O. (eds) Food Webs: Integration of Patterns and Dynamics. Chapman and Hall, New York, pp. 122-133 (1996)
    • (1996) Food Webs: Integration of Patterns and Dynamics , pp. 122-133
    • Arditi, R.1    Michalski, J.2
  • 11
    • 0000076167 scopus 로고
    • Mutual interference between parasites or predators and its effect on searching efficiency
    • Beddington, J.R.: Mutual interference between parasites or predators and its effect on searching efficiency. J. Anim. Ecol., 44, 331-340 (1975)
    • (1975) J. Anim. Ecol. , vol.44 , pp. 331-340
    • Beddington, J.R.1
  • 14
    • 33747057186 scopus 로고
    • The main topological part of plane vector fields with fixed Newton diagram
    • Le, D.T., Saito, K., Teissier, B. (eds), Word Scientific, Singapore, New Jersey, London, Hong Kong
    • Berezovskaya, F.S.: The main topological part of plane vector fields with fixed Newton diagram. In: Proceedings on Singularity Theory, Le, D.T., Saito, K., Teissier, B. (eds), Word Scientific, Singapore, New Jersey, London, Hong Kong. 55-73 (1995)
    • (1995) Proceedings on Singularity Theory , pp. 55-73
    • Berezovskaya, F.S.1
  • 15
    • 0001386483 scopus 로고
    • A complicated singular point of "center-focus" type and Newton diagram
    • Berezovskaya, F.S., Medvedeva, N.B.: A complicated singular point of "center-focus" type and Newton diagram. Selecta Mathematica formerly Sovietica, vol. 13(1), 1-15 (1994)
    • (1994) Selecta Mathematica Formerly Sovietica , vol.13 , Issue.1 , pp. 1-15
    • Berezovskaya, F.S.1    Medvedeva, N.B.2
  • 16
    • 0001394131 scopus 로고    scopus 로고
    • Variability, vagueness and comparison methods for ecological models
    • Cosner, C.: Variability, vagueness and comparison methods for ecological models. Bull. Math. Biol., 58, 207-246 (1996)
    • (1996) Bull. Math. Biol. , vol.58 , pp. 207-246
    • Cosner, C.1
  • 17
    • 0033180314 scopus 로고    scopus 로고
    • Effects of spatial grouping on the functional response of predators
    • Cosner, C., DeAngelis, D.L., Ault, J.S., Olson, D.B.: Effects of spatial grouping on the functional response of predators. Theor. Pop. Biol., 56, 65-75 (1999)
    • (1999) Theor. Pop. Biol. , vol.56 , pp. 65-75
    • Cosner, C.1    DeAngelis, D.L.2    Ault, J.S.3    Olson, D.B.4
  • 19
    • 0027132244 scopus 로고
    • Daphnia-phytoplankton interactions in lakes: Is there a need for pragmatic consumer-resource models?
    • Diehl, S., Lundberg, P.A., Gardfjell, H., Oksanen, L., Persson, L.: Daphnia-phytoplankton interactions in lakes: Is there a need for pragmatic consumer-resource models? Am. Nat., 142, 1052-1061 (1994)
    • (1994) Am. Nat. , vol.142 , pp. 1052-1061
    • Diehl, S.1    Lundberg, P.A.2    Gardfjell, H.3    Oksanen, L.4    Persson, L.5
  • 20
    • 0003015617 scopus 로고
    • Sur les cycles limites
    • Dulac, M.: Sur les cycles limites. Bull. Soc. Math. France. 51, 45-188 (1923)
    • (1923) Bull. Soc. Math. France , vol.51 , pp. 45-188
    • Dulac, M.1
  • 21
    • 0003061332 scopus 로고
    • Persistence in predator-prey systems with ratio-dependent predator influence
    • Freedman, H.I., Mathsen, R.M.: Persistence in predator-prey systems with ratio-dependent predator influence. Bull. Math. Biol., 55, 817-827 (1993)
    • (1993) Bull. Math. Biol. , vol.55 , pp. 817-827
    • Freedman, H.I.1    Mathsen, R.M.2
  • 22
    • 0001397558 scopus 로고
    • The functional response of predators: Worries about scale
    • Hanski, I.: The functional response of predators: worries about scale. Trends Ecol. Evol., 6, 141-142 (1991)
    • (1991) Trends Ecol. Evol. , vol.6 , pp. 141-142
    • Hanski, I.1
  • 23
    • 0014673629 scopus 로고
    • New inductive population model for insect parasites and its bearing on biological control
    • Hassell, M.P., Varley, C.C.: New inductive population model for insect parasites and its bearing on biological control. Nature, 223, 1133-1137 (1969)
    • (1969) Nature , vol.223 , pp. 1133-1137
    • Hassell, M.P.1    Varley, C.C.2
  • 24
    • 0035376255 scopus 로고    scopus 로고
    • Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system
    • in press
    • Hsu, S.-B., Hwang, T.-W., Kuang, Y.: Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system. J. Math. Biol. in press (2001)
    • (2001) J. Math. Biol.
    • Hsu, S.-B.1    Hwang, T.-W.2    Kuang, Y.3
  • 25
    • 0000809487 scopus 로고
    • Experimental studies on predation: Dispersion factors and predator-prey oscillations
    • Huffaker, C.B.: Experimental studies on predation: dispersion factors and predator-prey oscillations. Hilgardia, 27, 343-383 (1958)
    • (1958) Hilgardia , vol.27 , pp. 343-383
    • Huffaker, C.B.1
  • 26
    • 0033061694 scopus 로고    scopus 로고
    • About deterministic extinction in ratio-dependent predator-prey models
    • Jost, C., Arino, O., Arditi, R.: About deterministic extinction in ratio-dependent predator-prey models. Bull. Math. Biol., 61, 19-32 (1999)
    • (1999) Bull. Math. Biol. , vol.61 , pp. 19-32
    • Jost, C.1    Arino, O.2    Arditi, R.3
  • 27
    • 4544313738 scopus 로고
    • Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps
    • Khibnik, A.I., Kuznetsov, Yu.A., Levitin, V.V., Nikolaev, E.V.: Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps. Physica D, 62, 360-371 (1993)
    • (1993) Physica D , vol.62 , pp. 360-371
    • Khibnik, A.I.1    Kuznetsov, Yu.A.2    Levitin, V.V.3    Nikolaev, E.V.4
  • 28
    • 0000941262 scopus 로고    scopus 로고
    • Rich dynamics of Gause-type ratio-dependent predator-prey system
    • Kuang, Y.: Rich dynamics of Gause-type ratio-dependent predator-prey system. Fields Inst. Comm., 21, 325-337 (1999)
    • (1999) Fields Inst. Comm. , vol.21 , pp. 325-337
    • Kuang, Y.1
  • 29
    • 0000252357 scopus 로고    scopus 로고
    • Global qualitative analysis of a ratio-dependent predator-prey systems
    • Kuang, Y., Beretta, A.: Global qualitative analysis of a ratio-dependent predator-prey systems. J. Math. Biol., 35, 389-406 (1998)
    • (1998) J. Math. Biol. , vol.35 , pp. 389-406
    • Kuang, Y.1    Beretta, A.2
  • 30
    • 0003236870 scopus 로고
    • Elements of Applied Bifurcation Theory
    • Springer-Verlag, NY, Berlin, Heidelberg
    • Kuznetsov, Yu.A.: Elements of Applied Bifurcation Theory. Applied. Math. Sci., vol. 112. Springer-Verlag, NY, Berlin, Heidelberg (1995)
    • (1995) Applied. Math. Sci. , vol.112
    • Kuznetsov, Yu.A.1
  • 33
    • 0000386086 scopus 로고
    • Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum
    • Luckinbill, L.S.: Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum. Ecology, 54, 1320-1327 (1973)
    • (1973) Ecology , vol.54 , pp. 1320-1327
    • Luckinbill, L.S.1
  • 34
    • 0028887109 scopus 로고
    • Food web structure at equilibrium and far from it: Is it the same?
    • Michalski, J., Arditi, R.: Food web structure at equilibrium and far from it: is it the same? Proc. R. Soc. Lond. B. 259, 217-222 (1995)
    • (1995) Proc. R. Soc. Lond. B. , vol.259 , pp. 217-222
    • Michalski, J.1    Arditi, R.2
  • 35
    • 0031582205 scopus 로고    scopus 로고
    • Macroscopic dynamic effects of migration in patchy predator-prey systems
    • Michalski, J., Poggiale, J.-C., Arditi, R., Auger, P.M.: Macroscopic dynamic effects of migration in patchy predator-prey systems. J. Theor. Biol., 185, 459-474 (1997)
    • (1997) J. Theor. Biol. , vol.185 , pp. 459-474
    • Michalski, J.1    Poggiale, J.-C.2    Arditi, R.3    Auger, P.M.4
  • 36
    • 0031742563 scopus 로고    scopus 로고
    • Emergence of donor control in patchy predator-prey systems
    • Poggiale, J.-C., Michalski, J., Arditi, R.: Emergence of donor control in patchy predator-prey systems. Bull. Math. Biol., 60, 1149-1166 (1998)
    • (1998) Bull. Math. Biol. , vol.60 , pp. 1149-1166
    • Poggiale, J.-C.1    Michalski, J.2    Arditi, R.3
  • 37
    • 0142131847 scopus 로고
    • On mathematical models of elementary processes in biogeocoenosis
    • in Russian
    • Poletaev, I.A.: On mathematical models of elementary processes in biogeocoenosis. Problems of Cybernetics, No 16, 171-190 (1966) (in Russian).
    • (1966) Problems of Cybernetics , Issue.16 , pp. 171-190
    • Poletaev, I.A.1
  • 38
    • 0015243940 scopus 로고
    • Paradox of enrichment: Destabilization of exploitation systems in ecological time
    • Rosenzweig, M.L.: Paradox of enrichment: destabilization of exploitation systems in ecological time. Science 171, 385-387 (1971)
    • (1971) Science , vol.171 , pp. 385-387
    • Rosenzweig, M.L.1
  • 39
    • 0001475407 scopus 로고
    • The interpretation of tests for ratio-dependence
    • Ruxton, G.D., Gurney, W.S.C.: The interpretation of tests for ratio-dependence. Oikos, 65, 334-335 (1992)
    • (1992) Oikos , vol.65 , pp. 334-335
    • Ruxton, G.D.1    Gurney, W.S.C.2
  • 40
    • 0028003568 scopus 로고
    • Inferring process from pattern: Trophic-level abundances and imbedded interactions
    • Sarnelle, O.: Inferring process from pattern: trophic-level abundances and imbedded interactions. Ecology, 75, 1835-1841 (1994)
    • (1994) Ecology , vol.75 , pp. 1835-1841
    • Sarnelle, O.1


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