EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 6 / No 1 (2011) Math. Model. Nat. Phenom., 6 1 (2011) 163-187 References
Free Access
Issue
Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011
Instability and patterns. Issue dedicated to the memory of A. Golovin
Page(s) 163 - 187
DOI https://doi.org/10.1051/mmnp/20116109
Published online 09 June 2010
  1. M. Shachak, B. Boeken, E. Groner, R. Kadmon, Y. Lubin, E. Meron, E.G. Neeman, A. Perevolotsky, Y. Shkedy, E. Ungar. Woody species as landscape modulators and their effect on biodiversity patterns. BioScience, 58 (2008), 209–221. [CrossRef] [Google Scholar]
  2. M. Scheffer, S. Carpenter, J.A. Foley, C. Folke, B. Walkerk. Catastrophic shifts in ecosystems. Nature, 413 (2001), 591–596. [CrossRef] [PubMed] [Google Scholar]
  3. J. von Hardenberg, E. Meron, M. Shachak, Y. Zarmi. Diversity of Vegetation Patterns and Desertification. Phys. Rev. Lett., 87 (2001), 198101. [CrossRef] [PubMed] [Google Scholar]
  4. M. Rietkerk, S.C. Dekker, P.C. de Ruiter, J. van de Koppel. Self-organized patchiness and catastrophic shifts in ecosystems. Science, 305 (2004), 1926–1029. [CrossRef] [PubMed] [Google Scholar]
  5. M. Loreau, S. Naeem, P. Inchausti, J. Bengtsson, J.P. Grime, A. Hector, D.U. Hooper, M.A. Huston, D. Raffaelli, B. Schmid, D. Tilman, D.A. Wardle. Biodiversity and Ecosystem Functioning: Current Knowledge and Future Challenges. Science, 294 (2001), 804–808. [CrossRef] [PubMed] [Google Scholar]
  6. Millennium Ecosystem Assessment. Ecosystems and Human Well-being: Desertification Synthesis. World Resources Institute, Washington, DC. 2005. [Google Scholar]
  7. Millennium Ecosystem Assessment. Ecosystems and Human Well-being: Biodiversity Synthesis. World Resources Institute, Washington, DC. 2005. [Google Scholar]
  8. N. Barbier, P. Coutron, J. Lejoly, V. Deblauwe, O. Lejeune. Self-organized vegetation patterning as a fingerprint of climate and human impact on semi-arid ecosystems. Journal of Ecology, 94 (2006), 537–547. [CrossRef] [Google Scholar]
  9. N. Barbier, P. Coutron, R. Lefever, V. Deblauwe, O. Lejune. Spatial decoupling of facilitation and competition at the origin of gapped vegetation patterns. Ecology, 89 (2008), 1521–1531. [CrossRef] [PubMed] [Google Scholar]
  10. I. Stavi, H. Lavee, E.D. Ungar, P. Sarah. Ecogeomorphic feedbacks in semiarid rangelands: A review. Pedosphere, 19 (2009) 217-229. [CrossRef] [Google Scholar]
  11. F. Borgogno, P. D’Odorico, F. Laio, L. Ridolfi. Mathematical models of vegetation pattern formation in ecohydrology. Reviews of Geophysics, 47 (2009), RG1005. [CrossRef] [Google Scholar]
  12. C. Valentin, J.M. d’Herbès, J. Poesen. Soil and water components of banded vegetation patterns. Catena, 37 (1999), 1–24. [CrossRef] [Google Scholar]
  13. V. Deblauwe, N. Barbier, P. Couteron, O. Lejeune, J. Bogaert. The global biogeography of semi-arid periodic vegetation patterns. Global Ecol. Biogeogr., 17 (2008), 715–723. [CrossRef] [Google Scholar]
  14. E. Gilad, J. von Hardenberg, A. Provenzale, M. Shachak, E. Meron. Ecosystem Engineers: From Pattern Formation to Habitat Creation. Phys. Rev. Lett., 93 (2004), 0981051. [Google Scholar]
  15. E. Gilad, J. von Hardenberg, A. Provenzale, M. Shachak, E. Meron. A mathematical Model for Plants as Ecosystem Engineers. J. Theor. Biol., 244 (2007), 680–691. [CrossRef] [PubMed] [Google Scholar]
  16. E. Gilad, M. Shachak, E. Meron. Dynamics and spatial organization of plant communities in water limited systems. Theor. Pop. Biol., 72 (2007), 214–230. [CrossRef] [Google Scholar]
  17. A.Y. Kletter, J. von Hardenberg, E. Meron, A. Provenzale. Patterned vegetation and rainfall intermittency. J. Theor. Biol., 256 (2009), 574–583. [CrossRef] [PubMed] [Google Scholar]
  18. R. Matyssek, H. Schnyder, E.F. Elstner, J.C. Munch, H. Pretzsch, H. Sandermann. Growth and parasite defence in plants: the balance between resource sequestration and retention: in lieu of a guest editorial. Plant Biol., 4 (2002), 133-136. [CrossRef] [Google Scholar]
  19. P.M. Saco, G.R. Willgoose, G.R. Hancock. Eco-geomorphology of banded vegetation patterns in arid and semi-arid regions. Earth Syst. Sci.Hydrol., 11 (2007), 1717–1730. [CrossRef] [Google Scholar]
  20. S.E. Campbell, J.S. Seeler, S. Glolubic. Desert crust formation and soil stabilization. Arid Soil Res. and Rehab. 3 (1989), 217–228. [Google Scholar]
  21. N.E. West. Structure and function in microphytic soil crusts in wildland ecosystems of arid and semi-arid regions. Adv. Ecol. Res., 20 (1990), 179–223. [CrossRef] [Google Scholar]
  22. D.J. Eldridge, E. Zaady, M. Shachak. Infiltration through three contrasting biological soil crusts in patterned landscapes in the Negev, Israel. Catena, 40 (2000), 323–336. [CrossRef] [Google Scholar]
  23. S.C. Dekker, M. Rietkerk, M.F.P. Bierkens. Coupling microscale vegetation-soil water and macroscale vegetation-precipitation feedbacks in semiarid ecosystems. Global change biology, 34 (2007), 671–678. [CrossRef] [Google Scholar]
  24. S. Thompson, G. Katul, S. M. McMahon. Role of biomass spread in vegetation pattern formation within arid ecosystems. Water Resour. Res., 44 (2008), W10421. [Google Scholar]
  25. R. Nathan, R. Casagrandi. A simple mechanistic model of seed dispersal, predation and plant establishment: Janzen-Connell and beyond. Journal of Ecology, 92 (2004), 733. [CrossRef] [Google Scholar]
  26. C.S. Holling. The functional response of invertebrate predators to prey density. Mem. Entomol. Soc. Canada, 48 (1966), 1–86. [Google Scholar]
  27. M. Santillana, C. Dawson. A numerical approach to study the properties of solutions of the diffusive wave approximation of the shallow water equations. Computational Geosciences, 14 (2010), 31–53. [CrossRef] [MathSciNet] [Google Scholar]
  28. J.L. Vázquez. The porous medium equation. Mathematical theory. Oxford University Press, Oxford, 2006. [Google Scholar]
  29. E. Meron, E. Gilad, J. von Hardenberg, M. Shachak, Y. Zarmi. Vegetation Patterns Along a Rainfall Gradient. Chaos, Solitons and Fractals, 19 (2004), 367–376. [Google Scholar]
  30. E. Meron, E. Gilad. Dynamics of plant communities in drylands: A pattern formation approach. In Complex Population Dynamics: Nonlinear Modeling in Ecology, Epidemiology and Genetics. Eds: B. Blasius, J. Kurths, and L. Stone, p. 49–76, World-Scientific, 2007. [Google Scholar]
  31. M. Rietkerk, F. van den Bosch, J. van de Koppel. Site-specific properties and irreversible vegetation changes in semi-arid grazing systems. Oikos, 80 (1997), 241–252. [CrossRef] [Google Scholar]
  32. E. Meron, H. Yizhaq, E. Gilad. Localized structures in dryland vegetation: forms and functions. Chaos, 17 (2007), 037109. [CrossRef] [PubMed] [Google Scholar]
  33. M. Tlidi, R. Lefever, A. Vladimirov. 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, 2008. [Google Scholar]
  34. Y. Pomeau. Front motion, metastability and subcritical bifurcations in hydrodynamics. Physica D, 23 (1986), 3–11. [CrossRef] [Google Scholar]
  35. E. Knobloch. Spatially localized structures in dissipative systems: open problems. Nonlinearity, 21 (2008), T45-T60. [CrossRef] [Google Scholar]
  36. S. Kéfi, M. Rietkerk, C.L. Alados, Y. Pueyo, V.P. Papanastasis, A. ElAich, P.C. de Ruiter. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature, 449 (2007), 213–216. [CrossRef] [PubMed] [Google Scholar]
  37. T.M. Scanlon, K.C. Kelly, S.A. Levin, I. Rodriguez-Iturbe. Positive feedbacks promote power-law clustering of Kalahari vegetation. Nature, 449 (2007), 209–212. [CrossRef] [PubMed] [Google Scholar]
  38. J. von Hardenberg, A.Y. Kletter, H. Yizhaq, J. Nathan, E. Meron. Periodic vs. scale-free patterns in dryland vegetation. Proc. R. Soc. B, 277 (2010), 1771–1776. [CrossRef] [Google Scholar]
  39. H. Yizhaq, E. Gilad, E. Meron. Banded vegetation: Biological Productivity and Resilience. Physica A, 356 (2005), 139–144. [CrossRef] [Google Scholar]
  40. L.S. Tuckerman, D. Barkley. Bifurcation analysis of the Eckhaus instability. Physica D, 46 (1990), 57–86. [CrossRef] [MathSciNet] [Google Scholar]
  41. F.I. Pugnaire, M.T. Luque. Changes in plant interactions along a gradient of environmental stress. Oikos, 93 (2001), 42–49. [CrossRef] [Google Scholar]
  42. C. Holzapfel, K. Tielborger, H.A. Parag, J. Kigel, M. Sternberg. Annual plant-shrub interactions along an aridity gradient. Basic Appl. Ecol., 7 (2006), 268-279. [CrossRef] [Google Scholar]
  43. C.G. Jones, J.H Lawton, M. Shachak, Organisms as ecosystem engineers, Oikos, 69 (1994), 373–386. [CrossRef] [Google Scholar]
  44. C.G. Jones, J.H Lawton, M. Shachak. Positive and negative effects of organisms as ecosystem engineers. Ecology, 78 (1997), 1946–1957. [CrossRef] [Google Scholar]
  45. R.M. Callaway, L.R. Walker. Competition and facilitation: a synthetic approach to interactions in plant communities. Ecology, 78 (1997), 1958-1965. [CrossRef] [Google Scholar]
  46. F.T. Maestre, S. Bautista, J. Cortina. Positive, negative and net effects in grassŰshrub interactions in Mediterranean semiarid grasslands. Ecology, 84 (2003), 3186-3197. [CrossRef] [Google Scholar]
  47. C.M. Crain, M.D. Bertness M.D.. Ecosystem Engineering across Environmental Gradients: Implications for Conservation and Management. Bioscience, 56 (2006), 211–218. [CrossRef] [Google Scholar]
  48. See for example F. Ludwig, T.E. Dawson, H. Kroon, F. Berendse, H.H.T. Prins. Hydraulic lift in Acacia tortilis trees on an East African savanna. Oecologia, 134 (2003), 293-300. [PubMed] [Google Scholar]
  49. E. Gilad. Mathematical models for vegetation patterns and biodiversity. Ph.D. thesis, Ben-Gurion University (2006). [Google Scholar]
  50. E. Gilad, J. von-Hardenberg. A fast algorithm for convolution integrals with space and time variant kernels. Journal of Computational Physics, 216 (2006) 326–336. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.