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Volumn 48, Issue 6, 2004, Pages 647-671

Large amplification in stage-structured models: Arnol'd tongues revisited

Author keywords

Arnol'd tongues; External forcing; LPA model; Noise; Periodicity; Stage structured models

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; ECOSYSTEM; NONLINEAR SYSTEM; PERIODICITY; STATISTICS;

EID: 4344616305     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00285-004-0264-8     Document Type: Review
Times cited : (15)

References (60)
  • 2
    • 0016740371 scopus 로고
    • Dynamic Complexity in predator-prey models framed in difference equations
    • Beddington, J.R., Free, C.A., Lawton, J.H.: Dynamic Complexity in predator-prey models framed in difference equations. Nature 255, 58-60 (1975)
    • (1975) Nature , vol.255 , pp. 58-60
    • Beddington, J.R.1    Free, C.A.2    Lawton, J.H.3
  • 3
    • 0023527468 scopus 로고
    • The Theory and Classification of Outbreaks
    • Barbosa, P., Schultz, J.C. (eds.). San Diego: Academic Press
    • Berryman, A.A.: The Theory and Classification of Outbreaks. In: Barbosa, P., Schultz, J.C. (eds.). Insect Outbreaks, San Diego: Academic Press, 1987
    • (1987) Insect Outbreaks
    • Berryman, A.A.1
  • 4
    • 0000119153 scopus 로고
    • Food web connectance and feedback dominance, or does everything really depend on everything else?
    • Berryman, A.A.: Food web connectance and feedback dominance, or does everything really depend on everything else? OIKOS 68, 183-185 (1993)
    • (1993) OIKOS , vol.68 , pp. 183-185
    • Berryman, A.A.1
  • 5
    • 33845547630 scopus 로고    scopus 로고
    • Do Trophic Interactions Cause Population Cycles?
    • Berryman, A.A. (ed.), Oxford, UK: Oxford University Press
    • Berryman, A.A.: Do Trophic Interactions Cause Population Cycles? In: Berryman, A.A. (ed.), Population Cycles: The Case for Trophic Interactions, Oxford, UK: Oxford University Press, 2002
    • (2002) Population Cycles: The Case for Trophic Interactions
    • Berryman, A.A.1
  • 7
    • 0033046113 scopus 로고    scopus 로고
    • Resonance effects and outbreaks in ecological time series
    • Blarer, A., Doebeli, M.: Resonance effects and outbreaks in ecological time series. Ecol. Lett. 2, 167-177 (1999)
    • (1999) Ecol. Lett. , vol.2 , pp. 167-177
    • Blarer, A.1    Doebeli, M.2
  • 8
    • 0004022281 scopus 로고    scopus 로고
    • Sunderland, Massachusetts: Sinauer Associates Inc.
    • Caswell, H.: Matrix Population Models. Sunderland, Massachusetts: Sinauer Associates Inc., 2001
    • (2001) Matrix Population Models
    • Caswell, H.1
  • 9
    • 0023510713 scopus 로고
    • Population regulation in animals with complex life-histories: Formulation and analysis of the damselfly model
    • Crowley, P.H., Nisbet, R.M., Gurney, W.S.C., Lawton, J.H.: Population regulation in animals with complex life-histories: Formulation and analysis of the damselfly model. Adv. Ecol. Res. 17, 1-58 (1987)
    • (1987) Adv. Ecol. Res. , vol.17 , pp. 1-58
    • Crowley, P.H.1    Nisbet, R.M.2    Gurney, W.S.C.3    Lawton, J.H.4
  • 12
    • 0028976114 scopus 로고
    • Nonlinear Demographic Dynamics: Mathematical Models, Statistical Methods, and Biological Experiments
    • Dennis, B., Desharnais, R.A., Cushing, J.M., Costantino, R.F.: Nonlinear Demographic Dynamics: Mathematical Models, Statistical Methods, and Biological Experiments. Ecol. Monogr. 65, 261-281 (1995)
    • (1995) Ecol. Monogr. , vol.65 , pp. 261-281
    • Dennis, B.1    Desharnais, R.A.2    Cushing, J.M.3    Costantino, R.F.4
  • 13
    • 0002454064 scopus 로고
    • The incidence of infectious diseases under the influence of seasonal fluctuations
    • New York: Springer-Verlag
    • Dietz, K.: The incidence of infectious diseases under the influence of seasonal fluctuations. Lecture Notes: Biomathematics 11, New York: Springer-Verlag, 1976, pp. 1-15
    • (1976) Lecture Notes: Biomathematics , vol.11 , pp. 1-15
    • Dietz, K.1
  • 14
    • 0000523039 scopus 로고
    • Perturbation of a Hopf Bifurcation by an External Time-Periodic Forcing
    • Gambaudo, J.M.: Perturbation of a Hopf Bifurcation by an External Time-Periodic Forcing. J. Diff. Eqns. 57, 172-199 (1985)
    • (1985) J. Diff. Eqns. , vol.57 , pp. 172-199
    • Gambaudo, J.M.1
  • 15
    • 0031886729 scopus 로고    scopus 로고
    • Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree
    • Geritz, S.A.H., Kisdi, E., Meszena, G., Metz, J.A.J.: Evolutionary singular strategies and the adaptive growth and branching of the evolutionary tree. Evolutionary Ecology 12, 35-57 (1998)
    • (1998) Evolutionary Ecology , vol.12 , pp. 35-57
    • Geritz, S.A.H.1    Kisdi, E.2    Meszena, G.3    Metz, J.A.J.4
  • 16
    • 0028173753 scopus 로고
    • Population cycles of forest Lepidoptera: A maternal effect hypothesis
    • Ginzburg, L.R., Taneyhill, D.E.: Population cycles of forest Lepidoptera: a maternal effect hypothesis. J. Anim. Ecol. 63, 79-92 (1994)
    • (1994) J. Anim. Ecol. , vol.63 , pp. 79-92
    • Ginzburg, L.R.1    Taneyhill, D.E.2
  • 17
    • 0037323968 scopus 로고    scopus 로고
    • The amplification of environmental noise in population models: Causes and consequences
    • Greenman, J. V., Benton, T.G.: The amplification of environmental noise in population models: causes and consequences. Am. Nat. 161, 225-239 (2003)
    • (2003) Am. Nat. , vol.161 , pp. 225-239
    • Greenman, J.V.1    Benton, T.G.2
  • 18
    • 1142267538 scopus 로고    scopus 로고
    • External Forcing of Ecological and Epidemiological Systems: A resonance approach
    • Greenman, J.V., Kamo, M., Boots, M.: External Forcing of Ecological and Epidemiological Systems: a resonance approach. Physica D 190, 136-151 (2004)
    • (2004) Physica D , vol.190 , pp. 136-151
    • Greenman, J.V.1    Kamo, M.2    Boots, M.3
  • 19
    • 0017781629 scopus 로고
    • The dynamics of density dependent population models
    • Guckenheimer, J., Oster, J.G., Ipaktchi, A.: The dynamics of density dependent population models. J. Math. Biol. 4, 101-147 (1977)
    • (1977) J. Math. Biol. , vol.4 , pp. 101-147
    • Guckenheimer, J.1    Oster, J.G.2    Ipaktchi, A.3
  • 21
    • 0346684337 scopus 로고    scopus 로고
    • Multiple attractors and resonance in periodically forced population models
    • Henson, S.M.: Multiple attractors and resonance in periodically forced population models. Physica D 140, 33-49 (2000)
    • (2000) Physica D , vol.140 , pp. 33-49
    • Henson, S.M.1
  • 22
    • 0030616677 scopus 로고    scopus 로고
    • Stochastic Dynamics and Deterministic Skeletons: Population Behavior of Dungeness Crab
    • Higgins, K., Hastings, A., Sarvela, J.N., Botsford, L.W.: Stochastic Dynamics and Deterministic Skeletons: Population Behavior of Dungeness Crab. Science 276, 1431-1435 (1997)
    • (1997) Science , vol.276 , pp. 1431-1435
    • Higgins, K.1    Hastings, A.2    Sarvela, J.N.3    Botsford, L.W.4
  • 23
    • 0031977596 scopus 로고    scopus 로고
    • Small mammals cycles in northern Europe: Patterns and evidence for the maternal effect hypothesis
    • Inchausti, P., Ginzburg, L.R.: Small mammals cycles in northern Europe: patterns and evidence for the maternal effect hypothesis. J. Anim. Ecol. 67, 180-194 (1998)
    • (1998) J. Anim. Ecol. , vol.67 , pp. 180-194
    • Inchausti, P.1    Ginzburg, L.R.2
  • 24
    • 0030055277 scopus 로고    scopus 로고
    • Cyclic population dynamics and random perturbations
    • Kaitala, V., Ranta, E., Lindström, J.: Cyclic population dynamics and random perturbations. Ecology 65, 249-251 (1996)
    • (1996) Ecology , vol.65 , pp. 249-251
    • Kaitala, V.1    Ranta, E.2    Lindström, J.3
  • 25
    • 0033531771 scopus 로고    scopus 로고
    • Dynamic complexities in host-parasitoid interaction
    • Kaitala, V., Ylikarjula, J., Heino, M.: Dynamic complexities in host-parasitoid interaction. J. theor. Biol. 197, 331-341 (1999)
    • (1999) J. Theor. Biol. , vol.197 , pp. 331-341
    • Kaitala, V.1    Ylikarjula, J.2    Heino, M.3
  • 27
    • 1842815889 scopus 로고    scopus 로고
    • The macroecology of population dynamics: Taxonomic and biogeographic patterns in population cycles
    • Kendall, B.E., Prendergast, J., Bjornstad, O.N.: The macroecology of population dynamics: taxonomic and biogeographic patterns in population cycles. Ecol. Lett. 1, 160-164 (1998)
    • (1998) Ecol. Lett. , vol.1 , pp. 160-164
    • Kendall, B.E.1    Prendergast, J.2    Bjornstad, O.N.3
  • 29
    • 0033218990 scopus 로고    scopus 로고
    • The rainbow bridge: Hamiltonian limits and resonance in predator-prey dynamics
    • King, A.A., Schaffer, W.M.: The rainbow bridge: Hamiltonian limits and resonance in predator-prey dynamics. J. Math. Biol. 39, 439-469 (1999)
    • (1999) J. Math. Biol. , vol.39 , pp. 439-469
    • King, A.A.1    Schaffer, W.M.2
  • 30
    • 0035105763 scopus 로고    scopus 로고
    • The geometry of a population cycle: A mechanistic model of snowshoe hare demography
    • King, A.A., Schaffer, W.M.: The geometry of a population cycle: a mechanistic model of snowshoe hare demography. Ecology 82, 814-830 (2001)
    • (2001) Ecology , vol.82 , pp. 814-830
    • King, A.A.1    Schaffer, W.M.2
  • 31
    • 0035820190 scopus 로고    scopus 로고
    • The Effect of Evolution on Host-Parasitoid Systems
    • Kon, R., Takeuchi, Y.: The Effect of Evolution on Host-Parasitoid Systems. J. theor. Biol. 209, 287-302 (2001)
    • (2001) J. Theor. Biol. , vol.209 , pp. 287-302
    • Kon, R.1    Takeuchi, Y.2
  • 32
    • 0027978417 scopus 로고
    • Bifurcation analysis of periodic SEIR and SIR epidemic models
    • Kuznetsov, Y.A., Piccardi, C.: Bifurcation analysis of periodic SEIR and SIR epidemic models. J. Math. Biol. 32, 109-121 (1994)
    • (1994) J. Math. Biol. , vol.32 , pp. 109-121
    • Kuznetsov, Y.A.1    Piccardi, C.2
  • 35
    • 0003291236 scopus 로고
    • Two-dimensional iterative maps
    • A.V. Holden, (ed.), Manchester, UK: Manchester University Press
    • Lauwerier, H.A.: Two-dimensional iterative maps. In: A.V. Holden, (ed.), Chaos, Manchester, UK: Manchester University Press, 1986
    • (1986) Chaos
    • Lauwerier, H.A.1
  • 36
    • 77956980711 scopus 로고
    • On the use of matrices in certain population mathematics
    • Leslie, PH.: On the use of matrices in certain population mathematics. Biometrika 33, 213-245 (1945)
    • (1945) Biometrika , vol.33 , pp. 213-245
    • Leslie, P.H.1
  • 37
    • 0034481495 scopus 로고    scopus 로고
    • What causes outbreaks of the gypsy moth in North America?
    • Liebhold, A., Elkinton, J., Williams, D., Muzika, R.M.: What causes outbreaks of the gypsy moth in North America? Popul. Ecol. 42, 257-266 (2000)
    • (2000) Popul. Ecol. , vol.42 , pp. 257-266
    • Liebhold, A.1    Elkinton, J.2    Williams, D.3    Muzika, R.M.4
  • 38
    • 0034703768 scopus 로고    scopus 로고
    • Population dynamics of the yellow clam Mesodesma mactroides: Recruitment variability, density-dependence and stochastic processes
    • Lima, M., Brazeiro, A., Defeo, O.: Population dynamics of the yellow clam Mesodesma mactroides: recruitment variability, density-dependence and stochastic processes. Mar. Ecol. Prog. Ser. 207, 97-108 (2000)
    • (2000) Mar. Ecol. Prog. Ser. , vol.207 , pp. 97-108
    • Lima, M.1    Brazeiro, A.2    Defeo, O.3
  • 39
    • 0035039430 scopus 로고    scopus 로고
    • Origin of an insect outbreak: Escape in space or time from natural enemies?
    • Maron, J.E., Harrison, S., Greaves, M.: Origin of an insect outbreak: escape in space or time from natural enemies? Oecologia 126, 595-602 (2001)
    • (2001) Oecologia , vol.126 , pp. 595-602
    • Maron, J.E.1    Harrison, S.2    Greaves, M.3
  • 40
    • 0029705385 scopus 로고    scopus 로고
    • Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective
    • Marrow, P., Dieckmann, U., Law, R.: Evolutionary Dynamics of Predator-Prey Systems: An Ecological Perspective. J. Math. Biol. 34, 556-578 (1996)
    • (1996) J. Math. Biol. , vol.34 , pp. 556-578
    • Marrow, P.1    Dieckmann, U.2    Law, R.3
  • 41
    • 0016394337 scopus 로고
    • Biological populations with nonoverlapping generations: Stable points, stable cycles and chaos
    • May, R.M.: Biological populations with nonoverlapping generations: stable points, stable cycles and chaos. Science 186, 645-647 (1974)
    • (1974) Science , vol.186 , pp. 645-647
    • May, R.M.1
  • 42
    • 0017185443 scopus 로고
    • Simple mathematical models with very complicated dynamics
    • May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976)
    • (1976) Nature , vol.261 , pp. 459-467
    • May, R.M.1
  • 43
    • 0033540082 scopus 로고    scopus 로고
    • Large-amplitude cycles of Daphnia and its algal prey in enriched environments
    • McCauley, E., Nisbet, R.M., Murdoch, W.W., de Roos, A.M., Gurney, W.S.C.: Large-amplitude cycles of Daphnia and its algal prey in enriched environments. Nature 402, 653-656 (1999)
    • (1999) Nature , vol.402 , pp. 653-656
    • McCauley, E.1    Nisbet, R.M.2    Murdoch, W.W.3    De Roos, A.M.4    Gurney, W.S.C.5
  • 45
    • 0001125241 scopus 로고
    • Can a general hypothesis explain population cycles of forest Lepidoptera?
    • Myers, J.H.: Can a general hypothesis explain population cycles of forest Lepidoptera? Adv. Ecol. Res. 18, 179-242 (1988)
    • (1988) Adv. Ecol. Res. , vol.18 , pp. 179-242
    • Myers, J.H.1
  • 47
    • 0011504750 scopus 로고
    • On some cases of periodic motion depending on parameters
    • Neimark, Y.I.: On some cases of periodic motion depending on parameters. Dokl. Akad. Nauk SSSR 129, 736-739 (1959)
    • (1959) Dokl. Akad. Nauk SSSR , vol.129 , pp. 736-739
    • Neimark, Y.I.1
  • 48
    • 0034252135 scopus 로고    scopus 로고
    • Density-dependent vital rates and their population dynamic consequences
    • Neubert, M.G., Caswell, H.: Density-dependent vital rates and their population dynamic consequences. J. Math. Biol. 41, 103-121 (2000)
    • (2000) J. Math. Biol. , vol.41 , pp. 103-121
    • Neubert, M.G.1    Caswell, H.2
  • 50
    • 0000962996 scopus 로고
    • Population dynamic consequences of competition within and between age classes
    • Nisbet, R.M., Onyiah, L.C.: Population dynamic consequences of competition within and between age classes. J. Math. Biol. 32, 329-344 (1994)
    • (1994) J. Math. Biol. , vol.32 , pp. 329-344
    • Nisbet, R.M.1    Onyiah, L.C.2
  • 52
    • 0037737986 scopus 로고    scopus 로고
    • Natural enemy specialization and the period of population cycles
    • Rohani, P., Wearing, H.J., Cameron, T., Sait, S.M.: Natural enemy specialization and the period of population cycles. Ecol. Lett. 6, 381-384 (2003)
    • (2003) Ecol. Lett. , vol.6 , pp. 381-384
    • Rohani, P.1    Wearing, H.J.2    Cameron, T.3    Sait, S.M.4
  • 54
    • 84972537058 scopus 로고
    • On invariant surfaces and bifurcations of periodic solutions of ordinary differential equations
    • Sacker, R.S.: On invariant surfaces and bifurcations of periodic solutions of ordinary differential equations. Commun. Pure and Appl. Math. 18, 717-732 (1965)
    • (1965) Commun. Pure and Appl. Math. , vol.18 , pp. 717-732
    • Sacker, R.S.1
  • 55
    • 0030986178 scopus 로고    scopus 로고
    • Population regulation in snowshoe hare and Canadian lynx: Asymmetric food web configurations between hare and lynx
    • Stenseth, N.C., Falck, W., Bjornstad, O.N., Krebs, C.J.: Population regulation in snowshoe hare and Canadian lynx: Asymmetric food web configurations between hare and lynx. Proc. Natl. Acad. Sci. USA 94, 5147-5152 (1997)
    • (1997) Proc. Natl. Acad. Sci. USA , vol.94 , pp. 5147-5152
    • Stenseth, N.C.1    Falck, W.2    Bjornstad, O.N.3    Krebs, C.J.4
  • 57
    • 0002182259 scopus 로고
    • Population Dynamics in Variable Environments
    • New York: Springer-Verlag
    • Tuljapurkar, S.: Population Dynamics in Variable Environments. Lecture Notes in Biomathematics, vol. 85, New York: Springer-Verlag, 1990
    • (1990) Lecture Notes in Biomathematics , vol.85
    • Tuljapurkar, S.1
  • 58
    • 0025250821 scopus 로고
    • Rarity of density dependence or population regulation with lags?
    • Turchin, P.: Rarity of density dependence or population regulation with lags? Nature 344, 660-663 (1990)
    • (1990) Nature , vol.344 , pp. 660-663
    • Turchin, P.1
  • 60
    • 0004149831 scopus 로고    scopus 로고
    • Cambridge, UK: Cambridge University Press
    • Wolfram, S.: The Mathematica Book. Cambridge, UK: Cambridge University Press, 1999
    • (1999) The Mathematica Book
    • Wolfram, S.1


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