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Volumn 4, Issue 1, 2011, Pages 37-53

Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system

Author keywords

Excitability; Non Turing patterns; Predator prey system; Ratio dependence; Spatiotemporal chaos; Turing instability; Turing Hopf bifurcation

Indexed keywords

CHAOS THEORY; ECOLOGICAL MODELING; POPULATION DYNAMICS; PREDATION; PREDATOR-PREY INTERACTION; SELF ORGANIZATION; SPATIAL ANALYSIS; SPATIOTEMPORAL ANALYSIS;

EID: 85028093389     PISSN: 18741738     EISSN: 18741746     Source Type: Journal    
DOI: 10.1007/s12080-010-0073-1     Document Type: Article
Times cited : (141)

References (69)
  • 1
    • 0034255819 scopus 로고    scopus 로고
    • The nature of predation: prey dependent, ratio dependent or neither?
    • Abrams P, Ginzburg LR (2000) The nature of predation: prey dependent, ratio dependent or neither? TREE 15: 337-341.
    • (2000) Tree , vol.15 , pp. 337-341
    • Abrams, P.1    Ginzburg, L.R.2
  • 2
    • 4944258042 scopus 로고
    • Coupling in predator-prey dynamics: ratio-dependence
    • Arditi R, Ginzburg LR (1989) Coupling in predator-prey dynamics: ratio-dependence. J Theor Biol 139: 311-326.
    • (1989) J Theor Biol , vol.139 , pp. 311-326
    • Arditi, R.1    Ginzburg, L.R.2
  • 3
    • 14844315022 scopus 로고    scopus 로고
    • Ratio-dependent predator-prey model: effect of environmental fluctuation and stability
    • Bandyopadhyay M, Chattopadhyay J (2005) Ratio-dependent predator-prey model: effect of environmental fluctuation and stability. Nonlinearity 18: 913-936.
    • (2005) Nonlinearity , vol.18 , pp. 913-936
    • Bandyopadhyay, M.1    Chattopadhyay, J.2
  • 4
    • 0035368396 scopus 로고    scopus 로고
    • Self-organized spatial structures in a ratio-dependent predator-prey model
    • Bartumeus F, Alonso D, Catalana J (2001) Self-organized spatial structures in a ratio-dependent predator-prey model. Physica A 295: 53-57.
    • (2001) Physica A , vol.295 , pp. 53-57
    • Bartumeus, F.1    Alonso, D.2    Catalana, J.3
  • 5
    • 33847055875 scopus 로고    scopus 로고
    • Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations
    • Baurmann M, Gross T, Feudel U (2007) Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. J Theor Biol 245: 220-229.
    • (2007) J Theor Biol , vol.245 , pp. 220-229
    • Baurmann, M.1    Gross, T.2    Feudel, U.3
  • 6
    • 0035460669 scopus 로고    scopus 로고
    • Parametric analysis of the ratio-dependent predator-prey model
    • Berezovskaya FS, Karev G, Arditi R (2001) Parametric analysis of the ratio-dependent predator-prey model. J Math Biol 43: 221-246.
    • (2001) J Math Biol , vol.43 , pp. 221-246
    • Berezovskaya, F.S.1    Karev, G.2    Arditi, R.3
  • 7
    • 0027075622 scopus 로고
    • The origin and evolution of predator-prey theory
    • Berryman AA (1992) The origin and evolution of predator-prey theory. Ecology 73: 1530-1535.
    • (1992) Ecology , vol.73 , pp. 1530-1535
    • Berryman, A.A.1
  • 10
    • 0034886763 scopus 로고    scopus 로고
    • Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model
    • Couteron P, Lejeune O (2001) Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model. J Ecol 89: 616-628.
    • (2001) J Ecol , vol.89 , pp. 616-628
    • Couteron, P.1    Lejeune, O.2
  • 12
    • 0001069111 scopus 로고
    • Periodic fluctuations in the number of animals: their cause and effects
    • Elton CS (1924) Periodic fluctuations in the number of animals: their cause and effects. Brit J Exp Biol 2: 119-163.
    • (1924) Brit J Exp Biol , vol.2 , pp. 119-163
    • Elton, C.S.1
  • 13
    • 28244492039 scopus 로고    scopus 로고
    • Global asymptotic stability of a ratio-dependent predator-prey system with diffusion
    • Fan YH, Li WT (2006) Global asymptotic stability of a ratio-dependent predator-prey system with diffusion. J Comput Appl Math 188: 205-227.
    • (2006) J Comput Appl Math , vol.188 , pp. 205-227
    • Fan, Y.H.1    Li, W.T.2
  • 14
    • 0001944481 scopus 로고
    • The statistical and mathematical analysis of plankton patchiness
    • Fasham MJR (1978) The statistical and mathematical analysis of plankton patchiness. Oceanogr Mar Biol Ann Rev 16: 43-79.
    • (1978) Oceanogr Mar Biol Ann Rev , vol.16 , pp. 43-79
    • Fasham, M.J.R.1
  • 15
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • Fisher RA (1937) The wave of advance of advantageous genes. Ann Eugenics 7: 355-369.
    • (1937) Ann Eugenics , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 17
    • 0031662774 scopus 로고    scopus 로고
    • Circle and spiral: population persistence in a spatially explicit predator-prey model
    • Gurney WSC, Veith AR, Cruichshank I, McGeachin G (1998) Circle and spiral: population persistence in a spatially explicit predator-prey model. Ecology 79: 2516-2530.
    • (1998) Ecology , vol.79 , pp. 2516-2530
    • Gurney, W.S.C.1    Veith, A.R.2    Cruichshank, I.3    McGeachin, G.4
  • 18
    • 0028176208 scopus 로고
    • Partial differential equations in ecology: spatial interactions and population dynamics
    • Holmes EE, Lewis MA, Banks JE, Veit RR (1994) Partial differential equations in ecology: spatial interactions and population dynamics. Ecology 75: 17-29.
    • (1994) Ecology , vol.75 , pp. 17-29
    • Holmes, E.E.1    Lewis, M.A.2    Banks, J.E.3    Veit, R.R.4
  • 19
    • 0033604549 scopus 로고    scopus 로고
    • Biodiversity of plankton by oscillations and chaos
    • Huisman J, Weissing FJ (1999) Biodiversity of plankton by oscillations and chaos. Nature 402: 407-410.
    • (1999) Nature , vol.402 , pp. 407-410
    • Huisman, J.1    Weissing, F.J.2
  • 20
    • 0033061694 scopus 로고    scopus 로고
    • About deterministic extinction in ratio-dependent predator-prey model
    • Jost C, Arino O, Arditi R (1999) About deterministic extinction in ratio-dependent predator-prey model. Bull Math Biol 61: 19-32.
    • (1999) Bull Math Biol , vol.61 , pp. 19-32
    • Jost, C.1    Arino, O.2    Arditi, R.3
  • 21
    • 0001039597 scopus 로고
    • The size of water masses containing plankton blooms
    • Kierstead H, Slobodkin LB (1953) The size of water masses containing plankton blooms. J Mar Res 12: 141-147.
    • (1953) J Mar Res , vol.12 , pp. 141-147
    • Kierstead, H.1    Slobodkin, L.B.2
  • 22
    • 0033546065 scopus 로고    scopus 로고
    • Regular and irregular patterns in semiarid vegetation
    • Klausmeier CA (1999) Regular and irregular patterns in semiarid vegetation. Science 284: 1826-1828.
    • (1999) Science , vol.284 , pp. 1826-1828
    • Klausmeier, C.A.1
  • 25
    • 0000252357 scopus 로고    scopus 로고
    • Global qualitative analysis of a ratio-dependent predator-prey system
    • Kuang Y, Beretta E (1998) Global qualitative analysis of a ratio-dependent predator-prey system. J Math Biol 36: 389-406.
    • (1998) J Math Biol , vol.36 , pp. 389-406
    • Kuang, Y.1    Beretta, E.2
  • 26
    • 36849153282 scopus 로고
    • Hypothesis for origin of planktonic patchiness
    • Levin SA, Segel LA (1976) Hypothesis for origin of planktonic patchiness. Nature 259: 659.
    • (1976) Nature , vol.259 , pp. 659
    • Levin, S.A.1    Segel, L.A.2
  • 27
    • 0000386086 scopus 로고
    • Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum
    • Luckinbill LL (1973) Coexistence in laboratory populations of Paramecium aurelia and its predator Didinium nasutum. Ecology 54: 1320-1327.
    • (1973) Ecology , vol.54 , pp. 1320-1327
    • Luckinbill, L.L.1
  • 28
    • 0001256338 scopus 로고
    • The effects of space and enrichment on a predator-prey system
    • Luckinbill LL (1974) The effects of space and enrichment on a predator-prey system. Ecology 55: 1142-1147.
    • (1974) Ecology , vol.55 , pp. 1142-1147
    • Luckinbill, L.L.1
  • 31
    • 0027845917 scopus 로고
    • Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics
    • Malchow H (1993) Spatio-temporal pattern formation in nonlinear nonequilibrium plankton dynamics. Proc R Soc Lond B 251: 103-109.
    • (1993) Proc R Soc Lond B , vol.251 , pp. 103-109
    • Malchow, H.1
  • 36
    • 0001089850 scopus 로고    scopus 로고
    • Generic spatiotemporal dynamics near codimension-two Turing-Hopf bifurcations
    • Meixner M, De Wit A, Bose S, Scholl E (1997) Generic spatiotemporal dynamics near codimension-two Turing-Hopf bifurcations. Phys Rev E 55: 6690-6697.
    • (1997) Phys Rev E , vol.55 , pp. 6690-6697
    • Meixner, M.1    de Wit, A.2    Bose, S.3    Scholl, E.4
  • 37
    • 0001883519 scopus 로고
    • Pattern formation in excitable media
    • Meron E (1992) Pattern formation in excitable media. Phys Rep 218: 1-66.
    • (1992) Phys Rep , vol.218 , pp. 1-66
    • Meron, E.1
  • 38
    • 64449084527 scopus 로고    scopus 로고
    • Excitable population dynamics, biological control failure, and spatiotemporal pattern formation in a model ecosystem
    • Morozov AY, Petrovskii SV (2009) Excitable population dynamics, biological control failure, and spatiotemporal pattern formation in a model ecosystem. Bull Math Biol 71: 863-887.
    • (2009) Bull Math Biol , vol.71 , pp. 863-887
    • Morozov, A.Y.1    Petrovskii, S.V.2
  • 39
    • 3042846003 scopus 로고    scopus 로고
    • Bifurcation, chaos and intermittency in the predator-prey system with the Allee effect
    • Morozov AY, Petrovskii SV, Li BL (2004) Bifurcation, chaos and intermittency in the predator-prey system with the Allee effect. Proc R Soc Lond B 271: 1407-1414.
    • (2004) Proc R Soc Lond B , vol.271 , pp. 1407-1414
    • Morozov, A.Y.1    Petrovskii, S.V.2    Li, B.L.3
  • 40
    • 0000518462 scopus 로고    scopus 로고
    • Scenarios of domain pattern formation in a reaction-diffusion system
    • Muratov CB, Osipov VV (1996) Scenarios of domain pattern formation in a reaction-diffusion system. Phys Rev E 54: 4860-4879.
    • (1996) Phys Rev E , vol.54 , pp. 4860-4879
    • Muratov, C.B.1    Osipov, V.V.2
  • 42
  • 45
    • 0027806283 scopus 로고
    • Diffusion-induced chaos in a spatial predator-prey system
    • Pascual M (1993) Diffusion-induced chaos in a spatial predator-prey system. Proc R Soc Lond B 251: 1-7.
    • (1993) Proc R Soc Lond B , vol.251 , pp. 1-7
    • Pascual, M.1
  • 46
    • 0001102631 scopus 로고
    • Complex patterns in a simple system
    • Pearson JE (1993) Complex patterns in a simple system. Science 261: 189-192.
    • (1993) Science , vol.261 , pp. 189-192
    • Pearson, J.E.1
  • 48
    • 12944314880 scopus 로고    scopus 로고
    • Transition to spatiotemporal chaos can resolve the paradox of enrichment
    • Petrovskii SV, Li BL, Malchow H (2004) Transition to spatiotemporal chaos can resolve the paradox of enrichment. Ecol Complexity 1: 37-47.
    • (2004) Ecol Complexity , vol.1 , pp. 37-47
    • Petrovskii, S.V.1    Li, B.L.2    Malchow, H.3
  • 49
    • 0033120656 scopus 로고    scopus 로고
    • A minimal model of pattern formation in a prey-predator system
    • Petrovskii SV, Malchow H (1999) A minimal model of pattern formation in a prey-predator system. Math Comput Model 29: 49-63.
    • (1999) Math Comput Model , vol.29 , pp. 49-63
    • Petrovskii, S.V.1    Malchow, H.2
  • 50
    • 0035718414 scopus 로고    scopus 로고
    • Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics
    • Petrovskii SV, Malchow H (2001) Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics. Theor Popul Biol 59: 157-174.
    • (2001) Theor Popul Biol , vol.59 , pp. 157-174
    • Petrovskii, S.V.1    Malchow, H.2
  • 51
    • 0036113356 scopus 로고    scopus 로고
    • Allee effect makes possible patchy invasion in predator-prey system
    • Petrovskii SV, Morozov AY, Venturino E (2002) Allee effect makes possible patchy invasion in predator-prey system. Ecol Lett 5: 345-352.
    • (2002) Ecol Lett , vol.5 , pp. 345-352
    • Petrovskii, S.V.1    Morozov, A.Y.2    Venturino, E.3
  • 52
    • 0037406626 scopus 로고    scopus 로고
    • Quantification of the spatial aspect of chaotic dynamics in biological and chemical systems
    • Petrovskii SV, Li BL, Malchow H (2003) Quantification of the spatial aspect of chaotic dynamics in biological and chemical systems. Bull Math Biol 65: 425-446.
    • (2003) Bull Math Biol , vol.65 , pp. 425-446
    • Petrovskii, S.V.1    Li, B.L.2    Malchow, H.3
  • 53
    • 0015243940 scopus 로고
    • Paradox of enrichment: destabilization of exploitation ecosystem in ecological time
    • Rosenzweig ML (1971) Paradox of enrichment: destabilization of exploitation ecosystem in ecological time. Science 171: 385-387.
    • (1971) Science , vol.171 , pp. 385-387
    • Rosenzweig, M.L.1
  • 55
    • 0015442349 scopus 로고
    • Dissipative structure: an explanation and an ecological example
    • Segel LA, Jackson JL (1972) Dissipative structure: an explanation and an ecological example. J Theor Biol 37: 545-559.
    • (1972) J Theor Biol , vol.37 , pp. 545-559
    • Segel, L.A.1    Jackson, J.L.2
  • 57
    • 0035127918 scopus 로고    scopus 로고
    • Periodic travelling waves in cyclic predator-prey systems
    • Sherratt JA (2001) Periodic travelling waves in cyclic predator-prey systems. Ecol Lett 4: 30-37.
    • (2001) Ecol Lett , vol.4 , pp. 30-37
    • Sherratt, J.A.1
  • 58
    • 35649003882 scopus 로고    scopus 로고
    • The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reactiondiffusion systems
    • Sherratt JA, Smith MJ (2007) The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reactiondiffusion systems. Physica D 236: 90-103.
    • (2007) Physica D , vol.236 , pp. 90-103
    • Sherratt, J.A.1    Smith, M.J.2
  • 59
    • 40749098198 scopus 로고    scopus 로고
    • Periodic travelling waves in cyclic populations: field studies and reaction diffusion models
    • Sherratt JA, Smith M (2008) Periodic travelling waves in cyclic populations: field studies and reaction diffusion models. J R Soc Interface 5: 483-505.
    • (2008) J R Soc Interface , vol.5 , pp. 483-505
    • Sherratt, J.A.1    Smith, M.2
  • 61
    • 70449104849 scopus 로고    scopus 로고
    • Absolute stability of wavetrains can explain spatiotemporal dynamics in reaction-diffusion systems of lambda-omega type
    • Smith MJ, Rademacher JDM, Sherratt JA (2009) Absolute stability of wavetrains can explain spatiotemporal dynamics in reaction-diffusion systems of lambda-omega type. SIAM J Appl Dyn Sys 8: 1136-1159.
    • (2009) SIAM J Appl Dyn Sys , vol.8 , pp. 1136-1159
    • Smith, M.J.1    Rademacher, J.D.M.2    Sherratt, J.A.3
  • 63
    • 0028176205 scopus 로고
    • Competition and bioderversity in spatially structured habitats
    • Tilman D (1994) Competition and bioderversity in spatially structured habitats. Ecology 75: 2-16.
    • (1994) Ecology , vol.75 , pp. 2-16
    • Tilman, D.1
  • 64
    • 0028011510 scopus 로고
    • Ocean plankton populations as excitable media
    • Truscott JE, Brindley J (1994) Ocean plankton populations as excitable media. Bull Math Biol 56: 981-998.
    • (1994) Bull Math Biol , vol.56 , pp. 981-998
    • Truscott, J.E.1    Brindley, J.2
  • 66
    • 0002011401 scopus 로고
    • The chemical basis of morphogenesis
    • Turing AM (1952) The chemical basis of morphogenesis. Phil Trans R Soc Lond B 237: 37-72.
    • (1952) Phil Trans R Soc Lond B , vol.237 , pp. 37-72
    • Turing, A.M.1
  • 67
    • 70350566024 scopus 로고    scopus 로고
    • Reaction-diffusion waves in biology
    • Volpert V, Petrovskii SV (2009) Reaction-diffusion waves in biology. Phys Life Rev 6: 267-310.
    • (2009) Phys Life Rev , vol.6 , pp. 267-310
    • Volpert, V.1    Petrovskii, S.V.2
  • 68
    • 0035464834 scopus 로고    scopus 로고
    • Global dynamics of a ratio-dependent predator-prey systems
    • Xiao D, Ruan S (2001) Global dynamics of a ratio-dependent predator-prey systems. J Math Biol 43: 221-290.
    • (2001) J Math Biol , vol.43 , pp. 221-290
    • Xiao, D.1    Ruan, S.2


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