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Volumn 300, Issue , 2012, Pages 134-142

Front dynamics in a two-species competition model driven by Lévy flights

Author keywords

Anomalous diffusion; Fractional derivatives; Front dynamics; L vy flights; Lotka Volterra model

Indexed keywords

ANOMALY; BROWNIAN MOTION; COMPETITION (ECOLOGY); DIFFUSION; LOTKA-VOLTERRA MODEL; NUMERICAL MODEL; SPECIATION (BIOLOGY); THEORETICAL STUDY;

EID: 84856487942     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2012.01.022     Document Type: Article
Times cited : (29)

References (59)
  • 2
    • 34548677557 scopus 로고    scopus 로고
    • Fractional reproduction-dispersal equations and heavy tail dispersal kernels
    • Baeumer B., Kovács M., Meerschaert M.M. Fractional reproduction-dispersal equations and heavy tail dispersal kernels. Bull. Math. Biol. 2007, 69:2281-2297.
    • (2007) Bull. Math. Biol. , vol.69 , pp. 2281-2297
    • Baeumer, B.1    Kovács, M.2    Meerschaert, M.M.3
  • 3
    • 17044431499 scopus 로고    scopus 로고
    • Lévy trajectories of Peruvian purse-seiners as an indicator of the spatial distribution of anchovy (Engraulis ringens)
    • Bertrand S., Burgos J.M., Gerlotto F., Atiquipa J. Lévy trajectories of Peruvian purse-seiners as an indicator of the spatial distribution of anchovy (Engraulis ringens). ICES J. Mar. Sci. 2005, 62:477-482.
    • (2005) ICES J. Mar. Sci. , vol.62 , pp. 477-482
    • Bertrand, S.1    Burgos, J.M.2    Gerlotto, F.3    Atiquipa, J.4
  • 5
    • 84884611850 scopus 로고    scopus 로고
    • Human mobility and spatial disease dynamics
    • Wiley-VCH, H.G. Schuster (Ed.)
    • Brockmann D. Human mobility and spatial disease dynamics. Reviews of Nonlinear Dynamics and Complexity 2009, 1-24. Wiley-VCH. H.G. Schuster (Ed.).
    • (2009) Reviews of Nonlinear Dynamics and Complexity , pp. 1-24
    • Brockmann, D.1
  • 6
    • 35248828149 scopus 로고    scopus 로고
    • Fluid limit of the continuous-time random walk with general Lévy jump distribution functions
    • Cartea A., del Castillo Negrete D. Fluid limit of the continuous-time random walk with general Lévy jump distribution functions. Phys. Rev. E-Stat. Nonlinear Soft Matter Phys. 2007, 76:041105.
    • (2007) Phys. Rev. E-Stat. Nonlinear Soft Matter Phys. , vol.76 , pp. 041105
    • Cartea, A.1    del Castillo Negrete, D.2
  • 7
    • 33751093078 scopus 로고    scopus 로고
    • Fractional diffusion models of option prices in markets with jumps
    • Cartea A., del Castillo Negrete D. Fractional diffusion models of option prices in markets with jumps. Phys. A: Stat. Mech. Appl. 2007, 374:749-763.
    • (2007) Phys. A: Stat. Mech. Appl. , vol.374 , pp. 749-763
    • Cartea, A.1    del Castillo Negrete, D.2
  • 8
    • 0002745423 scopus 로고    scopus 로고
    • A fractional diffusion equation to describe Lévy flights
    • Chaves A.S. A fractional diffusion equation to describe Lévy flights. Phys. Lett. A 1998, 239:13-16.
    • (1998) Phys. Lett. A , vol.239 , pp. 13-16
    • Chaves, A.S.1
  • 9
    • 79952197225 scopus 로고    scopus 로고
    • A mathematical model on fractional Lotka-Volterra equations
    • Das S., Gupta P.K. A mathematical model on fractional Lotka-Volterra equations. J. Theor. Biol. 2011, 277:1-6.
    • (2011) J. Theor. Biol. , vol.277 , pp. 1-6
    • Das, S.1    Gupta, P.K.2
  • 10
    • 65349151299 scopus 로고    scopus 로고
    • Truncation effects in superdiffusive front propagation with Lévy flights
    • del Castillo Negrete D. Truncation effects in superdiffusive front propagation with Lévy flights. Phys. Rev. E 2009, 79:1-10.
    • (2009) Phys. Rev. E , vol.79 , pp. 1-10
    • del Castillo Negrete, D.1
  • 11
    • 0043210605 scopus 로고    scopus 로고
    • Front dynamics in reaction-diffusion systems with Lévy flights: a fractional diffusion approach
    • del Castillo Negrete D., Carreras B.A., Lynch V.E. Front dynamics in reaction-diffusion systems with Lévy flights: a fractional diffusion approach. Phys. Rev. Lett. 2003, 91.
    • (2003) Phys. Rev. Lett. , vol.91
    • del Castillo Negrete, D.1    Carreras, B.A.2    Lynch, V.E.3
  • 13
    • 18144375226 scopus 로고    scopus 로고
    • Nondiffusive transport in plasma turbulence: a fractional diffusion approach
    • del Castillo Negrete D., Carreras B.A., Lynch V.E. Nondiffusive transport in plasma turbulence: a fractional diffusion approach. Phys. Rev. Lett. 2005, 94.
    • (2005) Phys. Rev. Lett. , vol.94
    • del Castillo Negrete, D.1    Carreras, B.A.2    Lynch, V.E.3
  • 15
    • 0039149429 scopus 로고    scopus 로고
    • Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts
    • Ebert U., van Saarloos W. Front propagation into unstable states: universal algebraic convergence towards uniformly translating pulled fronts. Physica D 2000, 146:1-99.
    • (2000) Physica D , vol.146 , pp. 1-99
    • Ebert, U.1    van Saarloos, W.2
  • 17
    • 79959860811 scopus 로고    scopus 로고
    • Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals
    • Edwards A.M. Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals. Ecology 2011, 92:1247-1257.
    • (2011) Ecology , vol.92 , pp. 1247-1257
    • Edwards, A.M.1
  • 19
    • 33646097441 scopus 로고    scopus 로고
    • Pattern formation in a fractional reaction-diffusion system
    • Gafiychuk V., Datsko B. Pattern formation in a fractional reaction-diffusion system. Phys. A: Stat. Mech. Appl. 2006, 365:300-306.
    • (2006) Phys. A: Stat. Mech. Appl. , vol.365 , pp. 300-306
    • Gafiychuk, V.1    Datsko, B.2
  • 21
    • 55149099624 scopus 로고    scopus 로고
    • Turing pattern formation in the Brusselator model with superdiffusion
    • Golovin A.A., Matkowskyt B.J., Volpert V.A. Turing pattern formation in the Brusselator model with superdiffusion. SIAM J. Appl. Math. 2008, 69:251-272.
    • (2008) SIAM J. Appl. Math. , vol.69 , pp. 251-272
    • Golovin, A.A.1    Matkowskyt, B.J.2    Volpert, V.A.3
  • 22
    • 75949112770 scopus 로고    scopus 로고
    • A comparison of three Eulerian numerical methods for fractional-order transport models
    • Hanert E. A comparison of three Eulerian numerical methods for fractional-order transport models. Environ. Fluid Mech. 2010, 10:7-20. 10.1007/s10652-009-9145-4.
    • (2010) Environ. Fluid Mech. , vol.10 , pp. 7-20
    • Hanert, E.1
  • 23
    • 79954926078 scopus 로고    scopus 로고
    • On the numerical solution of space-time fractional diffusion models
    • Hanert E. On the numerical solution of space-time fractional diffusion models. Comput. Fluids 2011, 46:33-39. 10.1016/j.compfluid.2010.08.010.
    • (2011) Comput. Fluids , vol.46 , pp. 33-39
    • Hanert, E.1
  • 24
    • 79953170542 scopus 로고    scopus 로고
    • Front dynamics in fractional-order epidemic models
    • Hanert E., Schumacher E., Deleersnijder E. Front dynamics in fractional-order epidemic models. J. Theor. Biol. 2011, 279:9-16. 10.1016/j.jtbi.2011.03.012.
    • (2011) J. Theor. Biol. , vol.279 , pp. 9-16
    • Hanert, E.1    Schumacher, E.2    Deleersnijder, E.3
  • 25
    • 0032079056 scopus 로고    scopus 로고
    • The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model
    • Hosono Y. The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model. Bull. Math. Biol. 1998, 60:435-448.
    • (1998) Bull. Math. Biol. , vol.60 , pp. 435-448
    • Hosono, Y.1
  • 27
    • 79961124638 scopus 로고    scopus 로고
    • Assessing Lévy walks as models of animal foraging
    • James A., Planck M.J., Edwards A.M. Assessing Lévy walks as models of animal foraging. J. R. Soc. Interface 2011, 8:1233-1247.
    • (2011) J. R. Soc. Interface , vol.8 , pp. 1233-1247
    • James, A.1    Planck, M.J.2    Edwards, A.M.3
  • 28
    • 31444435831 scopus 로고    scopus 로고
    • Generalized Fick's law and fractional ADE for pollution transport in a river: detailed derivation
    • Kim S., Kavvas M.L. Generalized Fick's law and fractional ADE for pollution transport in a river: detailed derivation. J. Hydrol. Eng. 2006, 11:80-83.
    • (2006) J. Hydrol. Eng. , vol.11 , pp. 80-83
    • Kim, S.1    Kavvas, M.L.2
  • 29
    • 0030426365 scopus 로고    scopus 로고
    • Dispersal data and the spread of invading organisms
    • Kot M., Lewis M.A., van den Driessche P. Dispersal data and the spread of invading organisms. Ecology 1996, 77:2027-2042.
    • (1996) Ecology , vol.77 , pp. 2027-2042
    • Kot, M.1    Lewis, M.A.2    van den Driessche, P.3
  • 32
    • 0036729759 scopus 로고    scopus 로고
    • Spreading speed and linear determinacy for two-species competition models
    • Lewis M.A., Li B., Weinberger H.F. Spreading speed and linear determinacy for two-species competition models. J. Math. Biol. 2002, 45:219-233.
    • (2002) J. Math. Biol. , vol.45 , pp. 219-233
    • Lewis, M.A.1    Li, B.2    Weinberger, H.F.3
  • 33
    • 4244129908 scopus 로고
    • Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight
    • Mantegna R.N., Stanley H.E. Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight. Phys. Rev. Lett. 1994, 73:2946-2949.
    • (1994) Phys. Rev. Lett. , vol.73 , pp. 2946-2949
    • Mantegna, R.N.1    Stanley, H.E.2
  • 35
    • 0038710532 scopus 로고    scopus 로고
    • Spreading disease: integro-differential equations old and new
    • Medlock J., Kot M. Spreading disease: integro-differential equations old and new. Math. Biosci. 2003, 184:201-222.
    • (2003) Math. Biosci. , vol.184 , pp. 201-222
    • Medlock, J.1    Kot, M.2
  • 36
    • 0002641421 scopus 로고    scopus 로고
    • The random walk's guide to anomalous diffusion: a fractional dynamics approach
    • Metzler R., Klafter J. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys. Rep. 2000, 339:1-77.
    • (2000) Phys. Rep. , vol.339 , pp. 1-77
    • Metzler, R.1    Klafter, J.2
  • 37
    • 4043151477 scopus 로고    scopus 로고
    • The restaurant at the end of the random walk: recent development in the description of anomalous transport by fractional dynamics
    • Metzler R., Klafter J. The restaurant at the end of the random walk: recent development in the description of anomalous transport by fractional dynamics. J. Phys. A 2004, 37:161-208.
    • (2004) J. Phys. A , vol.37 , pp. 161-208
    • Metzler, R.1    Klafter, J.2
  • 43
    • 0037430330 scopus 로고    scopus 로고
    • Generalized Richards' equation to simulate water transport in unsaturated soils
    • Pachepsky Y., Timlin D., Rawls W. Generalized Richards' equation to simulate water transport in unsaturated soils. J. Hydrol. 2003, 272:3-13.
    • (2003) J. Hydrol. , vol.272 , pp. 3-13
    • Pachepsky, Y.1    Timlin, D.2    Rawls, W.3
  • 45
    • 61349186917 scopus 로고    scopus 로고
    • Matrix approach to discrete fractional calculus. II. Partial fractional differential equations
    • Podlubny I., Chechkin A., Skovranek T., Chen Y., Jara B.M.V. Matrix approach to discrete fractional calculus. II. Partial fractional differential equations. J. Comput. Phys. 2009, 228:3137-3153.
    • (2009) J. Comput. Phys. , vol.228 , pp. 3137-3153
    • Podlubny, I.1    Chechkin, A.2    Skovranek, T.3    Chen, Y.4    Jara, B.M.V.5
  • 46
    • 77952745361 scopus 로고    scopus 로고
    • Multiscale analysis of collective motion and decision-making in swarms: an advection-diffusion equation with memory approach
    • Raghib M., Levin S., Kevrekidis I. Multiscale analysis of collective motion and decision-making in swarms: an advection-diffusion equation with memory approach. J. Theor. Biol. 2010, 264:893-913.
    • (2010) J. Theor. Biol. , vol.264 , pp. 893-913
    • Raghib, M.1    Levin, S.2    Kevrekidis, I.3
  • 47
    • 55849107781 scopus 로고    scopus 로고
    • Free-flight odor tracking in drosophila is consistent with an optimal intermittent scale-free search
    • Reynolds A.M., Frye M.A. Free-flight odor tracking in drosophila is consistent with an optimal intermittent scale-free search. PLoS One 2007, 2:e354.
    • (2007) PLoS One , vol.2
    • Reynolds, A.M.1    Frye, M.A.2
  • 49
    • 36749102467 scopus 로고    scopus 로고
    • Honeybees perform optimal scale-free searching flights when attempting to locate a food source
    • Reynolds A.M., Smith A.D., Reynolds D.R., Carreck N.L., Osborne J.L. Honeybees perform optimal scale-free searching flights when attempting to locate a food source. J. Exp. Biol. 2007, 210:3763-3770.
    • (2007) J. Exp. Biol. , vol.210 , pp. 3763-3770
    • Reynolds, A.M.1    Smith, A.D.2    Reynolds, D.R.3    Carreck, N.L.4    Osborne, J.L.5
  • 53
    • 0142119503 scopus 로고    scopus 로고
    • Front propagation into unstable states
    • van Saarloos W. Front propagation into unstable states. Phys. Rep. 2003, 386:29-222.
    • (2003) Phys. Rep. , vol.386 , pp. 29-222
    • van Saarloos, W.1
  • 54
    • 49849093656 scopus 로고    scopus 로고
    • Lévy flights and superdiffusion in the context of biological encounters and random searches
    • Viswanathan G., Raposo E., da Luz M. Lévy flights and superdiffusion in the context of biological encounters and random searches. Phys. Life Rev. 2008, 5:133-150.
    • (2008) Phys. Life Rev. , vol.5 , pp. 133-150
    • Viswanathan, G.1    Raposo, E.2    da Luz, M.3
  • 57
    • 70350566024 scopus 로고    scopus 로고
    • Reaction-diffusion waves in biology
    • Volpert V., Petrovskii S. Reaction-diffusion waves in biology. Phys. Life Rev. 2009, 6:267-310.
    • (2009) Phys. Life Rev. , vol.6 , pp. 267-310
    • Volpert, V.1    Petrovskii, S.2
  • 58
    • 0036725475 scopus 로고    scopus 로고
    • Analysis of linear determinacy for spread in cooperative models
    • Weinberger H.F., Lewis M.A., Li B. Analysis of linear determinacy for spread in cooperative models. J. Math. Biol. 2002, 45:183-218.
    • (2002) J. Math. Biol. , vol.45 , pp. 183-218
    • Weinberger, H.F.1    Lewis, M.A.2    Li, B.3
  • 59
    • 34547299910 scopus 로고    scopus 로고
    • Anomalous spreading speeds of cooperative recursion systems
    • Weinberger H.F., Lewis M.A., Li B. Anomalous spreading speeds of cooperative recursion systems. J. Math. Biol. 2007, 55:207-222.
    • (2007) J. Math. Biol. , vol.55 , pp. 207-222
    • Weinberger, H.F.1    Lewis, M.A.2    Li, B.3


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