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Volumn 67, Issue 6-7, 2013, Pages 1741-1764

Seasonal forcing and multi-year cycles in interacting populations: Lessons from a predator-prey model

Author keywords

Bifurcation diagram; Cyclic populations; Multi year cycles; Predator prey; Seasonal forcing; Subharmonics

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BIOLOGICAL RHYTHM; COMPUTER SIMULATION; ECOSYSTEM; POPULATION DYNAMICS; PREDATION; SEASON;

EID: 84887496178     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-012-0612-z     Document Type: Article
Times cited : (39)

References (52)
  • 2
    • 56649091320 scopus 로고    scopus 로고
    • Allometric scaling and seasonality in the epidemics of wildlife diseases
    • Bolzoni L, Dobson A, Gatto M, De Leo GA (2008) Allometric scaling and seasonality in the epidemics of wildlife diseases. Am Nat 172: 818-828.
    • (2008) Am Nat , vol.172 , pp. 818-828
    • Bolzoni, L.1    Dobson, A.2    Gatto, M.3    De Leo, G.A.4
  • 3
    • 74049165067 scopus 로고    scopus 로고
    • The interaction of seasonal forcing and immunity and the resonance dynamics of malaria
    • Childs DZ, Boots M (2010) The interaction of seasonal forcing and immunity and the resonance dynamics of malaria. J R Soc Interface 7: 309-319.
    • (2010) J R Soc Interface , vol.7 , pp. 309-319
    • Childs, D.Z.1    Boots, M.2
  • 4
    • 33750037356 scopus 로고    scopus 로고
    • Dynamics of infectious diseases and pulse vaccination: teasing apart the embedded resonance effects
    • Choisy M, Guegan JF, Rohani P (2006) Dynamics of infectious diseases and pulse vaccination: teasing apart the embedded resonance effects. Phys D 223: 26-35.
    • (2006) Phys D , vol.223 , pp. 26-35
    • Choisy, M.1    Guegan, J.F.2    Rohani, P.3
  • 5
    • 40949139796 scopus 로고    scopus 로고
    • Remarks on metacommunity synchronization with application to prey-predator systems
    • Colombo A, Dercole F, Rinaldi S (2008) Remarks on metacommunity synchronization with application to prey-predator systems. Am Nat 171: 430-442.
    • (2008) Am Nat , vol.171 , pp. 430-442
    • Colombo, A.1    Dercole, F.2    Rinaldi, S.3
  • 6
    • 0002454064 scopus 로고
    • The incidence of infectious disease under the influence of seasonal fluctuations
    • Springer, Berlin
    • Dietz K (1976) The incidence of infectious disease under the influence of seasonal fluctuations. In: Lecture notes in biomathematics: mathematical models in medicine, vol 11. Springer, Berlin, pp 1-15.
    • (1976) Lecture notes in biomathematics: Mathematical models in medicine , vol.11 , pp. 1-15
    • Dietz, K.1
  • 7
    • 0001755071 scopus 로고
    • AUTO: a program for the automatic bifurcation analysis of autonomous systems
    • Doedel EJ (1981) AUTO: a program for the automatic bifurcation analysis of autonomous systems. Congr Numer 30: 265-384.
    • (1981) Congr Numer , vol.30 , pp. 265-384
    • Doedel, E.J.1
  • 8
    • 0038194270 scopus 로고    scopus 로고
    • AUTO-07P: continuation and bifurcation software for ordinary differential equations
    • Doedel EJ, Oldeman BE (2009) AUTO-07P: continuation and bifurcation software for ordinary differential equations. Manual. http://indy. cs. concordia. ca/auto.
    • (2009) Manual
    • Doedel, E.J.1    Oldeman, B.E.2
  • 9
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems: (I) bifurcation in finite dimensions
    • Doedel EJ, Keller HB, Kernevez JP (1991) Numerical analysis and control of bifurcation problems: (I) bifurcation in finite dimensions. Int J Bifurcat Chaos 1: 493-520.
    • (1991) Int J Bifurcat Chaos , vol.1 , pp. 493-520
    • Doedel, E.J.1    Keller, H.B.2    Kernevez, J.P.3
  • 12
    • 10044287073 scopus 로고    scopus 로고
    • Dynamical resonance can account for seasonality of influenza epidemics
    • Dushoff J, Plotkin J, Levin S, Earn D (2004) Dynamical resonance can account for seasonality of influenza epidemics. Proc Natl Acad Sci USA 101: 16915-16916.
    • (2004) Proc Natl Acad Sci USA , vol.101 , pp. 16915-16916
    • Dushoff, J.1    Plotkin, J.2    Levin, S.3    Earn, D.4
  • 13
    • 0034723248 scopus 로고    scopus 로고
    • A simple model for complex dynamical transitions in epidemics
    • Earn DJD, Rohani P, Bolker BM, Grenfell BT (2000) A simple model for complex dynamical transitions in epidemics. Science 287: 667-670.
    • (2000) Science , vol.287 , pp. 667-670
    • Earn, D.J.D.1    Rohani, P.2    Bolker, B.M.3    Grenfell, B.T.4
  • 14
    • 0034360414 scopus 로고    scopus 로고
    • Time series modelling of childhood diseases: a dynamical systems approach
    • Finkenstadt BF, Grenfell BT (2000) Time series modelling of childhood diseases: a dynamical systems approach. J R Stat Soc Ser C Appl Stat 49: 187-205.
    • (2000) J R Stat Soc Ser C Appl Stat , vol.49 , pp. 187-205
    • Finkenstadt, B.F.1    Grenfell, B.T.2
  • 16
    • 0028854032 scopus 로고
    • A universal bifurcation diagram for seasonally perturbed predator-prey models
    • Gragnani A, Rinaldi S (1995) A universal bifurcation diagram for seasonally perturbed predator-prey models. Bull Math Biol 57: 701-712.
    • (1995) Bull Math Biol , vol.57 , pp. 701-712
    • Gragnani, A.1    Rinaldi, S.2
  • 17
    • 4344616305 scopus 로고    scopus 로고
    • Large amplification in stage-structured models: Arnol'd tongues revisited
    • Greenman JV, Benton TG (2004) Large amplification in stage-structured models: Arnol'd tongues revisited. J Math Biol 48: 647-671.
    • (2004) J Math Biol , vol.48 , pp. 647-671
    • Greenman, J.V.1    Benton, T.G.2
  • 18
    • 34250636321 scopus 로고    scopus 로고
    • Environmental forcing, invasion and control of ecological and epidemiological systems
    • Greenman J, Norman R (2007) Environmental forcing, invasion and control of ecological and epidemiological systems. J Theor Biol 247: 492-506.
    • (2007) J Theor Biol , vol.247 , pp. 492-506
    • Greenman, J.1    Norman, R.2
  • 19
    • 79952987784 scopus 로고    scopus 로고
    • Phase control of resonant systems: interference, chaos and high periodicity
    • Greenman JV, Pasour VB (2011) Phase control of resonant systems: interference, chaos and high periodicity. J Theor Biol 278: 74-86.
    • (2011) J Theor Biol , vol.278 , pp. 74-86
    • Greenman, J.V.1    Pasour, V.B.2
  • 20
    • 1142267538 scopus 로고    scopus 로고
    • External forcing of ecological and epidemiological systems: a resonance approach
    • Greenman JV, Kamo M, Boots M (2004) External forcing of ecological and epidemiological systems: a resonance approach. Phys D 190: 135-151.
    • (2004) Phys D , vol.190 , pp. 135-151
    • Greenman, J.V.1    Kamo, M.2    Boots, M.3
  • 22
    • 0027337545 scopus 로고
    • Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos
    • Hanski I, Turchin P, Korpimaki E, Henttonen H (1993) Population oscillations of boreal rodents: regulation by mustelid predators leads to chaos. Nature 364: 232-235.
    • (1993) Nature , vol.364 , pp. 232-235
    • Hanski, I.1    Turchin, P.2    Korpimaki, E.3    Henttonen, H.4
  • 24
    • 34547666538 scopus 로고    scopus 로고
    • Epidemiological effects of seasonal oscillations in birth rates
    • He D, Earn DJD (2007) Epidemiological effects of seasonal oscillations in birth rates. Theor Popul Biol 72: 274-291.
    • (2007) Theor Popul Biol , vol.72 , pp. 274-291
    • He, D.1    Earn, D.J.D.2
  • 25
    • 0030811684 scopus 로고    scopus 로고
    • A differential equation model of the interaction between the migration of the Senegalese grasshopper, Oedaleus senegalensis, its predators, and a seasonal habitat
    • Holt J, Colvin J (1997) A differential equation model of the interaction between the migration of the Senegalese grasshopper, Oedaleus senegalensis, its predators, and a seasonal habitat. Ecol Model 101: 185-193.
    • (1997) Ecol Model , vol.101 , pp. 185-193
    • Holt, J.1    Colvin, J.2
  • 26
    • 4544370028 scopus 로고    scopus 로고
    • The effect of seasonal host birth rates on population dynamics: the importance of resonance
    • Ireland JM, Norman RA, Greenman JV (2004) The effect of seasonal host birth rates on population dynamics: the importance of resonance. J Theor Biol 231: 229-238.
    • (2004) J Theor Biol , vol.231 , pp. 229-238
    • Ireland, J.M.1    Norman, R.A.2    Greenman, J.V.3
  • 29
    • 0033218990 scopus 로고    scopus 로고
    • The rainbow bridge: Hamitonian limits and resonance in predator-prey dynamics
    • King AA, Schaffer WM (1999) The rainbow bridge: Hamitonian limits and resonance in predator-prey dynamics. J Math Biol 39: 439-469.
    • (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 AA, Schaffer WM (2001) The geometry of a population cycle: a mechanistic model of snowshoe hare demography. Ecology 82: 814-830.
    • (2001) Ecology , vol.82 , pp. 814-830
    • King, A.A.1    Schaffer, W.M.2
  • 31
    • 0031716366 scopus 로고    scopus 로고
    • Experimental reduction of predators reverses the crash phase of small-rodent cycles
    • Korpimaki E, Norrdahl K (1998) Experimental reduction of predators reverses the crash phase of small-rodent cycles. Ecology 79: 2448-2455.
    • (1998) Ecology , vol.79 , pp. 2448-2455
    • Korpimaki, E.1    Norrdahl, K.2
  • 32
    • 0037157017 scopus 로고    scopus 로고
    • Dynamic effects of predators on cyclic voles: field experimentation and model extrapolation
    • Korpimaki E, Norrdahl K, Klemola T, Petterson T, Stenseth NC (2002) Dynamic effects of predators on cyclic voles: field experimentation and model extrapolation. Proc R Soc B 269: 991-997.
    • (2002) Proc R Soc B , vol.269 , pp. 991-997
    • Korpimaki, E.1    Norrdahl, K.2    Klemola, T.3    Petterson, T.4    Stenseth, N.C.5
  • 34
    • 0027978417 scopus 로고
    • Bifurcation analysis of periodic SEIR and SIR epidemic models
    • Kuznetsov YA, Piccardi C (1994) Bifurcation analysis of periodic SEIR and SIR epidemic models. J Math Biol 32: 109-121.
    • (1994) J Math Biol , vol.32 , pp. 109-121
    • Kuznetsov, Y.A.1    Piccardi, C.2
  • 35
  • 36
    • 0036252851 scopus 로고    scopus 로고
    • Belyakov homoclinic bifurcations in a tritrophic food chain model
    • Kuznetsov YA, De Feo O, Rinaldi S (2001) Belyakov homoclinic bifurcations in a tritrophic food chain model. SIAM J Appl Math 62: 462-487.
    • (2001) SIAM J Appl Math , vol.62 , pp. 462-487
    • Kuznetsov, Y.A.1    De Feo, O.2    Rinaldi, S.3
  • 37
    • 84755161354 scopus 로고    scopus 로고
    • Predation as a probable mechanism relating winter weather to population dynamics in a North American Porcupine population
    • Mabille G, Descamps S, Berteaux D (2010) Predation as a probable mechanism relating winter weather to population dynamics in a North American Porcupine population. Popul Ecol 52: 537-546.
    • (2010) Popul Ecol , vol.52 , pp. 537-546
    • Mabille, G.1    Descamps, S.2    Berteaux, D.3
  • 38
    • 0347360390 scopus 로고    scopus 로고
    • Computation of frequency locking regions for a discontinuous periodically forced reactor
    • Mancusi E, Russo L, Continillo G, Crescitelli S (2004) Computation of frequency locking regions for a discontinuous periodically forced reactor. Comput Chem Eng 28: 187-194.
    • (2004) Comput Chem Eng , vol.28 , pp. 187-194
    • Mancusi, E.1    Russo, L.2    Continillo, G.3    Crescitelli, S.4
  • 39
    • 0023496567 scopus 로고
    • Cyclic and stable populations: plankton as paradigm
    • McCauley E, Murdoch WW (1987) Cyclic and stable populations: plankton as paradigm. Am Nat 129: 97-121.
    • (1987) Am Nat , vol.129 , pp. 97-121
    • McCauley, E.1    Murdoch, W.W.2
  • 40
    • 0033540082 scopus 로고    scopus 로고
    • Large-amplitude cycles of Daphnia and its algal prey in enriched environments
    • McCauley E, Nisbet RM, Murdoch WW, de Roos AM, Gurney W (1999) Large-amplitude cycles of Daphnia and its algal prey in enriched environments. Nature 402: 653-656.
    • (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.5
  • 41
  • 42
    • 0027880626 scopus 로고
    • Conditioned chaos in seasonally perturbed predator-prey models
    • Rinaldi S, Muratori S (1993) Conditioned chaos in seasonally perturbed predator-prey models. Ecol Model 69: 79-97.
    • (1993) Ecol Model , vol.69 , pp. 79-97
    • Rinaldi, S.1    Muratori, S.2
  • 43
    • 2942676278 scopus 로고
    • Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities
    • Rinaldi S, Muratori S, Kuznetsov YA (1993) Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities. Bull Math Biol 55: 15-35.
    • (1993) Bull Math Biol , vol.55 , pp. 15-35
    • Rinaldi, S.1    Muratori, S.2    Kuznetsov, Y.A.3
  • 44
    • 0001524523 scopus 로고
    • Graphical representation and stability conditions of predator-prey interactions
    • Rosenzweig M, MacArthur R (1963) Graphical representation and stability conditions of predator-prey interactions. Am Nat 97: 209-223.
    • (1963) Am Nat , vol.97 , pp. 209-223
    • Rosenzweig, M.1    MacArthur, R.2
  • 45
    • 0343026677 scopus 로고    scopus 로고
    • Sub-harmonic resonance and multi-annual oscillations in Northern Mammals: a non-linear dynamical systems perspective
    • Schaffer WM, Pederson BS, Moore BK, Sharpaas O, King AA, Bronnikova TV (2001) Sub-harmonic resonance and multi-annual oscillations in Northern Mammals: a non-linear dynamical systems perspective. Chaos Soliton Fract 12: 251-264.
    • (2001) Chaos Soliton Fract , vol.12 , pp. 251-264
    • Schaffer, W.M.1    Pederson, B.S.2    Moore, B.K.3    Sharpaas, O.4    King, A.A.5    Bronnikova, T.V.6
  • 46
    • 0031446525 scopus 로고    scopus 로고
    • Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system
    • Scheffer M, Rinaldi S, Kuznetsov YA, van Nes EH (1997) Seasonal dynamics of Daphnia and algae explained as a periodically forced predator-prey system. OIKOS 80: 519-532.
    • (1997) OIKOS , vol.80 , pp. 519-532
    • Scheffer, M.1    Rinaldi, S.2    Kuznetsov, Y.A.3    van Nes, E.H.4
  • 48
    • 38849133690 scopus 로고    scopus 로고
    • Disease effects on reproduction can cause population cycles in seasonal environments
    • Smith MJ, White A, Sherratt JA, Telfer S, Begon M, Lambin X (2008) Disease effects on reproduction can cause population cycles in seasonal environments. J Anim Ecol 77: 378-389.
    • (2008) J Anim Ecol , vol.77 , pp. 378-389
    • Smith, M.J.1    White, A.2    Sherratt, J.A.3    Telfer, S.4    Begon, M.5    Lambin, X.6
  • 49
    • 0002314631 scopus 로고    scopus 로고
    • Seasonal forcing on the dynamics of Clethrionomys rufocanus: modeling geographic gradients in population dynamics
    • Stenseth NC, Bjornstad ON, Saitoh T (1998) Seasonal forcing on the dynamics of Clethrionomys rufocanus: modeling geographic gradients in population dynamics. Res Popul Ecol 40: 85-95.
    • (1998) Res Popul Ecol , vol.40 , pp. 85-95
    • Stenseth, N.C.1    Bjornstad, O.N.2    Saitoh, T.3
  • 51
    • 0030620326 scopus 로고    scopus 로고
    • An empirically based model for latitudinal gradient in vole population dynamics
    • Turchin P, Hanski I (1997) An empirically based model for latitudinal gradient in vole population dynamics. Am Nat 149: 842-874.
    • (1997) Am Nat , vol.149 , pp. 842-874
    • Turchin, P.1    Hanski, I.2
  • 52
    • 0842310300 scopus 로고    scopus 로고
    • Oscillatory reaction-diffusion equations with temporally varying parameters
    • Webb SD, Sherratt JA (2004) Oscillatory reaction-diffusion equations with temporally varying parameters. Math Comput Model 39: 45-60.
    • (2004) Math Comput Model , vol.39 , pp. 45-60
    • Webb, S.D.1    Sherratt, J.A.2


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