메뉴 건너뛰기




Volumn 242, Issue 1, 2013, Pages 30-41

Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments III: The transition between homoclinic solutions

Author keywords

Brousse tigr e; Homoclinic; Limit cycle; Mathematical model; Pattern formation; Perturbation theory; Reaction diffusion advection

Indexed keywords

ADVECTION; ARID REGIONS; DIFFUSION IN LIQUIDS; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES;

EID: 84869487584     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2012.08.014     Document Type: Article
Times cited : (42)

References (44)
  • 1
    • 0032796361 scopus 로고    scopus 로고
    • Soil and water components of banded vegetation patterns
    • C. Valentin, J.M. d'Herbès, and J. Poesen Soil and water components of banded vegetation patterns Catena 37 1999 1 24
    • (1999) Catena , vol.37 , pp. 1-24
    • Valentin, C.1    D'Herbès, J.M.2    Poesen, J.3
  • 2
    • 4644316410 scopus 로고    scopus 로고
    • Self-organized patchiness and catastrophic shifts in ecosystems
    • M. Rietkerk, S.C. Dekker, P.C. de Ruiter, and J. van de Koppel Self-organized patchiness and catastrophic shifts in ecosystems Science 305 2004 1926 1929
    • (2004) Science , vol.305 , pp. 1926-1929
    • Rietkerk, M.1    Dekker, S.C.2    De Ruiter, P.C.3    Van De Koppel, J.4
  • 3
    • 0036619703 scopus 로고    scopus 로고
    • Oblique vegetation banding in the Australian arid zone: Implications for theories of pattern evolution and maintenance
    • D.L. Dunkerley, and K.J. Brown Oblique vegetation banding in the Australian arid zone: implications for theories of pattern evolution and maintenance J. Arid. Environ. 52 2002 163 181
    • (2002) J. Arid. Environ. , vol.52 , pp. 163-181
    • Dunkerley, D.L.1    Brown, K.J.2
  • 4
    • 3242731295 scopus 로고    scopus 로고
    • Patterned mulga near Alice Springs, central Australia, and the potential threat of firewood collection on this vegetation community
    • S.S. Berg, and D.L. Dunkerley Patterned mulga near Alice Springs, central Australia, and the potential threat of firewood collection on this vegetation community J. Arid. Environ. 59 2004 313 350
    • (2004) J. Arid. Environ. , vol.59 , pp. 313-350
    • Berg, S.S.1    Dunkerley, D.L.2
  • 5
    • 0026593637 scopus 로고
    • The colonization of bare areas in two-phase mosaics of an arid ecosystem
    • C. Montaña The colonization of bare areas in two-phase mosaics of an arid ecosystem J. Ecol. 80 1992 315 327
    • (1992) J. Ecol. , vol.80 , pp. 315-327
    • Montaña, C.1
  • 6
    • 61649093834 scopus 로고    scopus 로고
    • Ecohydrological interactions within banded vegetation in the northeastern Chihuahuan Desert, USA
    • A.K. McDonald, R.J. Kinucan, and L.E. Loomis Ecohydrological interactions within banded vegetation in the northeastern Chihuahuan Desert, USA Ecohydrology 2 2009 66 71
    • (2009) Ecohydrology , vol.2 , pp. 66-71
    • McDonald, A.K.1    Kinucan, R.J.2    Loomis, L.E.3
  • 7
    • 0000402713 scopus 로고
    • Vegetation patterns in the semi-desert plains of British Somaliland
    • W. MacFadyen Vegetation patterns in the semi-desert plains of British Somaliland Geogr. J. 115 1950 199 211
    • (1950) Geogr. J. , vol.115 , pp. 199-211
    • MacFadyen, W.1
  • 8
    • 0032776192 scopus 로고    scopus 로고
    • Niger tiger bush as a natural water harvesting system
    • C. Valentin, and J.M. d'Herbès Niger tiger bush as a natural water harvesting system Catena 37 1999 231 256
    • (1999) Catena , vol.37 , pp. 231-256
    • Valentin, C.1    D'Herbès, J.M.2
  • 9
    • 0034210855 scopus 로고    scopus 로고
    • Differences between banded thickets (tiger bush) at two sites in West Africa
    • P. Couteron, A. Mahamane, P. Ouedraogo, and J. Seghieri Differences between banded thickets (tiger bush) at two sites in West Africa J. Veg. Sci. 11 2000 321 328
    • (2000) J. Veg. Sci. , vol.11 , pp. 321-328
    • Couteron, P.1    Mahamane, A.2    Ouedraogo, P.3    Seghieri, J.4
  • 10
    • 67649209518 scopus 로고    scopus 로고
    • Mathematical models of vegetation pattern formation in ecohydrology
    • Art. No. RG1005
    • F. Borgogno, P. D'Odorico, F. Laio, and L. Ridolfi Mathematical models of vegetation pattern formation in ecohydrology Rev. Geophys. 47 2009 Art. No. RG1005
    • (2009) Rev. Geophys. , vol.47
    • Borgogno, F.1    D'Odorico, P.2    Laio, F.3    Ridolfi, L.4
  • 11
  • 12
    • 0034886763 scopus 로고    scopus 로고
    • Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model
    • P. Couteron, and O. Lejeune Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model J. Ecol. 89 2001 616 628
    • (2001) J. Ecol. , vol.89 , pp. 616-628
    • Couteron, P.1    Lejeune, O.2
  • 13
    • 54249148731 scopus 로고    scopus 로고
    • Spatial decoupling of facilitation, competition at the origin of gapped vegetation patterns
    • N. Barbier, P. Couteron, R. Lefever, V. Deblauwe, and O. Lejeune Spatial decoupling of facilitation, competition at the origin of gapped vegetation patterns Ecology 89 2008 1521 1531
    • (2008) Ecology , vol.89 , pp. 1521-1531
    • Barbier, N.1    Couteron, P.2    Lefever, R.3    Deblauwe, V.4    Lejeune, O.5
  • 14
    • 70349776044 scopus 로고    scopus 로고
    • Deeply gapped vegetation patterns: On crown/root allometry, criticality and desertification
    • R. Lefever, N. Barbier, P. Couteron, and O. Lejeune Deeply gapped vegetation patterns: on crown/root allometry, criticality and desertification J. Theoret. Biol. 261 2009 194 209
    • (2009) J. Theoret. Biol. , vol.261 , pp. 194-209
    • Lefever, R.1    Barbier, N.2    Couteron, P.3    Lejeune, O.4
  • 15
    • 0028975325 scopus 로고
    • A model simulating the genesis of banded vegetation patterns in Niger
    • J.M. Thiéry, J.-M. D'Herbès, and C. Valentin A model simulating the genesis of banded vegetation patterns in Niger J. Ecol. 83 1995 497 507
    • (1995) J. Ecol. , vol.83 , pp. 497-507
    • Thiéry, J.M.1    D'Herbès, J.-M.2    Valentin, C.3
  • 16
    • 0028161461 scopus 로고
    • Simulating the dynamics of a vegetation mosaic: A spatialized functional model
    • A. Mauchamp, S. Rambal, and J. Lepart Simulating the dynamics of a vegetation mosaic: a spatialized functional model Ecol. Modell. 71 1994 107 130
    • (1994) Ecol. Modell. , vol.71 , pp. 107-130
    • Mauchamp, A.1    Rambal, S.2    Lepart, J.3
  • 17
    • 0030618625 scopus 로고    scopus 로고
    • Banded vegetation: Development under uniform rainfall from a simple cellular automaton model
    • D.L. Dunkerley Banded vegetation: development under uniform rainfall from a simple cellular automaton model Plant Ecol. 129 1997 103 111
    • (1997) Plant Ecol. , vol.129 , pp. 103-111
    • Dunkerley, D.L.1
  • 18
    • 0033546065 scopus 로고    scopus 로고
    • Regular and irregular patterns in semiarid vegetation
    • C.A. Klausmeier Regular and irregular patterns in semiarid vegetation Science 284 1999 1826 1828
    • (1999) Science , vol.284 , pp. 1826-1828
    • Klausmeier, C.A.1
  • 19
    • 22844447274 scopus 로고    scopus 로고
    • An analysis of vegetation stripe formation in semi-arid landscapes
    • J.A. Sherratt An analysis of vegetation stripe formation in semi-arid landscapes J. Math. Biol. 51 2005 183 197
    • (2005) J. Math. Biol. , vol.51 , pp. 183-197
    • Sherratt, J.A.1
  • 24
    • 34249109135 scopus 로고    scopus 로고
    • Modeling banded vegetation patterns in semiarid regions: Inter-dependence between biomass growth rate and relevant hydrological processes
    • N. Ursino Modeling banded vegetation patterns in semiarid regions: inter-dependence between biomass growth rate and relevant hydrological processes Water Resour. Res. 43 2007 W04412
    • (2007) Water Resour. Res. , vol.43 , pp. 04412
    • Ursino, N.1
  • 25
    • 64949124496 scopus 로고    scopus 로고
    • Above and below ground biomass patterns in arid lands
    • N. Ursino Above and below ground biomass patterns in arid lands Ecol. Modell. 220 2009 1411 1418
    • (2009) Ecol. Modell. , vol.220 , pp. 1411-1418
    • Ursino, N.1
  • 26
    • 77953835291 scopus 로고    scopus 로고
    • Measurement of self-organization in arid ecosystems
    • G.-Q. Sun, Z. Jin, and Q. Tan Measurement of self-organization in arid ecosystems J. Biol. Syst. 18 2010 495 508
    • (2010) J. Biol. Syst. , vol.18 , pp. 495-508
    • Sun, G.-Q.1    Jin, Z.2    Tan, Q.3
  • 27
    • 33749400238 scopus 로고    scopus 로고
    • Stability of banded vegetation patterns under seasonal rainfall and limited soil moisture storage capacity
    • N. Ursino, and S. Contarini Stability of banded vegetation patterns under seasonal rainfall and limited soil moisture storage capacity Adv. Water Resour. 29 2006 1556 1564
    • (2006) Adv. Water Resour. , vol.29 , pp. 1556-1564
    • Ursino, N.1    Contarini, S.2
  • 28
    • 34548442919 scopus 로고    scopus 로고
    • Self-organisation and productivity in semi-arid ecosystems: Implications of seasonality in rainfall
    • V. Guttal, and C. Jayaprakash Self-organisation and productivity in semi-arid ecosystems: implications of seasonality in rainfall J. Theoret. Biol. 248 2007 290 500
    • (2007) J. Theoret. Biol. , vol.248 , pp. 290-500
    • Guttal, V.1    Jayaprakash, C.2
  • 31
    • 52049091249 scopus 로고    scopus 로고
    • Dispersal strategies and spatial organization of vegetation in arid ecosystems
    • Y. Pueyo, S. Kefi, C.L. Alados, and M. Rietkerk Dispersal strategies and spatial organization of vegetation in arid ecosystems Oikos 117 2008 1522 1532
    • (2008) Oikos , vol.117 , pp. 1522-1532
    • Pueyo, Y.1    Kefi, S.2    Alados, C.L.3    Rietkerk, M.4
  • 32
    • 55949120162 scopus 로고    scopus 로고
    • Vegetation pattern shift as a result of rising atmospheric CO2 in arid ecosystems
    • S. Kefi, M. Rietkerk, and G.G. Katul Vegetation pattern shift as a result of rising atmospheric CO2 in arid ecosystems Theor. Popul. Biol. 74 2008 332 344
    • (2008) Theor. Popul. Biol. , vol.74 , pp. 332-344
    • Kefi, S.1    Rietkerk, M.2    Katul, G.G.3
  • 34
    • 0001896948 scopus 로고    scopus 로고
    • Theories on the origins, maintenance, dynamics, and functioning of banded landscapes
    • D.J. Tongway, C. Valentin, J. Seghieri, Springer New York
    • D.J. Tongway, and J.A. Ludwig Theories on the origins, maintenance, dynamics, and functioning of banded landscapes D.J. Tongway, C. Valentin, J. Seghieri, Banded Vegetation Patterning in Arid and Semi-Arid Environments 2001 Springer New York 20 31
    • (2001) Banded Vegetation Patterning in Arid and Semi-Arid Environments , pp. 20-31
    • Tongway, D.J.1    Ludwig, J.A.2
  • 35
    • 0001507360 scopus 로고    scopus 로고
    • Vegetation dynamics: Recruitment, regeneration in two-phase mosaics
    • D.J. Tongway, C. Valentin, J. Seghieri, Springer New York
    • C. Montaña, J. Seghieri, and A. Cornet Vegetation dynamics: recruitment, regeneration in two-phase mosaics D.J. Tongway, C. Valentin, J. Seghieri, Banded Vegetation Patterning in Arid and Semi-Arid Environments 2001 Springer New York 132 145
    • (2001) Banded Vegetation Patterning in Arid and Semi-Arid Environments , pp. 132-145
    • Montaña, C.1    Seghieri, J.2    Cornet, A.3
  • 36
  • 37
    • 33750998491 scopus 로고    scopus 로고
    • Nonlinear dynamics, pattern bifurcations in a model for vegetation stripes in semi-arid environments
    • J.A. Sherratt, and G.J. Lord Nonlinear dynamics, pattern bifurcations in a model for vegetation stripes in semi-arid environments Theor. Popul. Biol. 71 2007 1 11
    • (2007) Theor. Popul. Biol. , vol.71 , pp. 1-11
    • Sherratt, J.A.1    Lord, G.J.2
  • 38
    • 80755130540 scopus 로고    scopus 로고
    • Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments II: Patterns with the largest possible propagation speeds
    • J.A. Sherratt Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments II: patterns with the largest possible propagation speeds Proc. R. Soc. Lond. Ser. A 467 2011 3272 3294
    • (2011) Proc. R. Soc. Lond. Ser. A , vol.467 , pp. 3272-3294
    • Sherratt, J.A.1
  • 39
    • 0001755071 scopus 로고
    • AUTO, a program for the automatic bifurcation analysis of autonomous systems
    • E.J. Doedel AUTO, a program for the automatic bifurcation analysis of autonomous systems Congr. Numer. 30 1981 265 384
    • (1981) Congr. Numer. , vol.30 , pp. 265-384
    • Doedel, E.J.1
  • 40
    • 0000378937 scopus 로고
    • Numerical analysis and control of bifurcation problems: (I) bifurcation in finite dimensions
    • E.J. Doedel, H.B. Keller, and J.P. Kernévez Numerical analysis and control of bifurcation problems: (I) bifurcation in finite dimensions Internat. J. Bifur. Chaos 1 1991 493 520
    • (1991) Internat. J. Bifur. Chaos , vol.1 , pp. 493-520
    • Doedel, E.J.1    Keller, H.B.2    Kernévez, J.P.3
  • 41
    • 77958055560 scopus 로고    scopus 로고
    • Numerical continuation of branch points of equilibria and periodic orbits
    • E.J. Doedel, G. Domokos, I.G. Kevrekidis, World Scientific
    • E.J. Doedel, W. Govaerts, Y.A. Kuznetsov, and A. Dhooge Numerical continuation of branch points of equilibria and periodic orbits E.J. Doedel, G. Domokos, I.G. Kevrekidis, Modelling and Computations in Dynamical Systems 2006 World Scientific 145 164
    • (2006) Modelling and Computations in Dynamical Systems , pp. 145-164
    • Doedel, E.J.1    Govaerts, W.2    Kuznetsov, Y.A.3    Dhooge, A.4
  • 42
    • 78149344290 scopus 로고    scopus 로고
    • Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments i
    • J.A. Sherratt Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments I Nonlinearity 23 2010 2657 2675
    • (2010) Nonlinearity , vol.23 , pp. 2657-2675
    • Sherratt, J.A.1
  • 43
    • 0001811061 scopus 로고
    • Odepack a systematized collection of ODE solvers
    • R.S. Stepleman, North-Holland Amsterdam
    • A.C. Hindmarsh Odepack a systematized collection of ODE solvers R.S. Stepleman, Scientific Computing 1983 North-Holland Amsterdam 55 64
    • (1983) Scientific Computing , pp. 55-64
    • Hindmarsh, A.C.1
  • 44
    • 0000536084 scopus 로고
    • Automatic selection of methods for solving stiff, nonstiff systems of ordinary differential equations
    • L.R. Petzold Automatic selection of methods for solving stiff, nonstiff systems of ordinary differential equations SIAM J. Sci. Stat. Comput. 4 1983 136 148
    • (1983) SIAM J. Sci. Stat. Comput. , vol.4 , pp. 136-148
    • Petzold, L.R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.