Abstract
We present a model and nonlinear analysis which account for the clustering behaviors of arid vegetation ecosystems, the formation of localized bare soil spots (sometimes also called fairy circles) in these systems and the attractive or repulsive interactions governing their spatio-temporal evolution. Numerical solutions of the model closely agree with analytical predictions.
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References
P. Greig-Smith, J. Ecol. 67, 755 (1979).
for a survey of this phenomenon, see e.g. Catena. 1999. The significance of Soil, Water and Landscape Processes in Banded Vegetation Patterning. 37, Special Issue, C. Valentin and J. Poesen (Editors). D. J. Tongway, C. Valentin and J. Seghieri, Banded Vegetation Patterning in Arid and Semiarid Environments, (Springer-Verlag, New York, 2001).
R. Lefever and O. Lejeune, Bull. Math. Biol. 59, 263 (1997).
O. Lejeune, P. Couteron, and R. Lefever, Acta Oecologica 20, 171 (1999).
R. Lefever, O. Lejeune, and P. Couteron, in: Mathematical Models for Biological Pattern Formation. IMA Volumes in Mathematics and its Applications, Frontiers in Applied Mathematics Series 121, edited by H. Othmer and P. Maini, (Springer-Verlag, New York, 2000).
J. von Hardenberg, E. Meron, M. Shachak, and Y. Zarmi, Phys. Rev. Lett. 87, 198101 (2001).
T. Okayasu and Y. Aizawa, Prog. Theor. Phys. 106, 705 (2001).
R. HilleRisLambers, M. Rietkerk, F. van den Bosch, H.H.T. Prins, and H. de Kroon, Ecology, 82, 50 (2001).
E. Gilad, J. von Hardenberg, A. Provenzale, M. Shachak, and E. Meron, Phys. Rev. Lett. 93, 098105 (2004).
N.M. Shnerb, P. Sarah, H. Lavee, and S. Solomon, Phys. Rev. Lett. 90, 038101 (2003).
M. Rietkerk, M. C. Boerlijst, F. Van Langevelde, R. HillRisLambers, J. van de Koppel, L. Kumar, H.H.T. Prins, and A.M. Roos, Am. Nat., 160, 524 (2002).
M. Rietkerk, S.C. Dekker, P.C. de Ruiter, and J. van de Koppel, Science 305, 1926 (2004).
O. Lejeune, M. Tlidi, and R. Lefever, Int. J. Quantum Chem. 98, 261 (2004).
O. Lejeune, M. Tlidi, and P. Couteron, Phys. Rev. E 66, 010901(R) (2002).
E. Meron, E. Gilad, J. Von Hardenberg, M. Shachak, and Y. Zami, Chaos Solitons Fractals, 19, 367 (2004).
M.W. van Rooyen, G. K. Theron, N. van Rooyen, W.J. Jankowitz, and W.S. Matthews, J. Arid Environ. 57, 467 (2004).
K.A. Gorshkov and L.A. Ostrovsky, Physica D, 3, 428 (1981).
L.S. Aranson and K.A. Gorshkov, Physica D, 43, 435 (1990).
V.V. Afanasjev and N. Akhmediev, Phys. Rev. E 53, 6471 (1996).
N. Akhmediev, A. Ankiewicz, and J.M. Soto-Crespo, Phys. Rev. Lett. 79, 4047 (1997).
H.U. Bödeker, A.W. Liehr, T.D. Frank, R. Friedrich, and H.G. Purwins, New J. Phys. 6, 62 (2004).
A.G. Vladimirov, G.H. Khodova, and N.N. Rosanov, Phys. Rev. E 63, 056607 (2001).
M. Tlidi, A.G. Vladimirov, and P. Mandel, IEEE J. Quant. Elec. 39, 216 (2003).
A.G. Vladimirov, J.O. McSloy, D.V. Skryabin, and W. Firth, Phys. Rev. E 65, 064606 (2002).
R.M. Callaway and L. R. Walker, Ecology 78, 1958 (1997).
R. Lefever, N. Barbier, P. Couteron, and O. Lejeune, J. Ecology in preparation.
C.A. Klausmeier, Science 284, 1826 (1999).
J.A. Sherratt, J. Math. Biol. 51, 183 (2005).
R. Lefever, Bull. Cl. Sci. Acad. Roy. Belgique XV, 287 (2004).
R. Lefever, N. Barbier, P. Couteron, V. Deblauwe et O. Lejeune, Pour la Science - Dossier n 44, 68 (2004).
O. Lejeune and M. Tlidi, J. Veg. Sci. 10, 201 (1999); P. Couteron and O. Lejeune, J. Ecol. 89, 616 (2004).
S. Koga and Y. Kuramoto, Prog. Theor. Phys. 63, 106 (1980).
Y. Pomeau, Physica D, 23, 3 (1986).
S. Fauve and O. Thual, Phys. Rev. Lett. 64, 282 (1990).
M. Tlidi, P. Mandel, and R. Lefever, Phys. Rev. Lett. 73, 640 (1994).
V.B. Taranenko, K. Staliunas, and C.O. Weiss, Phys. Rev. A 56, 1582 (1997).
J. Boissonade, P. De Kepper, F. Gauffre, and I. Szalai, Chaos 16, 037110 (2006).
V.K. Vanag and I. R. Epstein, Phys. Rev. Lett. 92, 128301 (2004).
S. Barland, J. R. Tredicce, M. Brambilla, L.A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jägeet, Nature 419, 699 (2002).
U. Bortolozzo, M.G. Clerc, C. Falcon, S. Residori, and R. Rojas, Phys. Rev. Lett. 96, 214501 (2006).
M. Pesch, E. Groβe Westhoff, T. Ackemann, and W. Lange, Phys. Rev. Lett. 95, 143906 (2005).
L. Yu. Glebsky and L.M. Lerman, Chaos 5, 424 (1995).
G.W. Hunt, G.J. Lord, and A.R. Champneys, Compt. Methods Appl. Mech. Eng. 170, 239 (1999).
P. Coullet, C. Riera, and C. Tresser, Phys. Rev. Lett. 84, 3069 (2000).
J. Burke and E. Knobloch, Phys. Rev. E 73, 056211 (2006).
G. Kozyreff and S.J. Chapman, Phys. Rev. Lett. 97, 044502 (2006).
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Tlidi, M., Lefever, R., Vladimirov, A. (2008). On Vegetation Clustering, Localized Bare Soil Spots and Fairy Circles. In: Dissipative Solitons: From Optics to Biology and Medicine. Lecture Notes in Physics, vol 751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78217-9_15
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DOI: https://doi.org/10.1007/978-3-540-78217-9_15
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