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Discrete Dynamics in Nature and Society
Volume 2015 (2015), Article ID 185432, 15 pages
http://dx.doi.org/10.1155/2015/185432
Research Article

Analysis of Spatiotemporal Dynamic and Bifurcation in a Wetland Ecosystem

1School of Mathematics and Information Science, Wenzhou University, Wenzhou, Zhejiang 325035, China
2Zhejiang Provincial Key Laboratory for Water Environment and Marine Biological Resources Protection, Wenzhou University, Wenzhou, Zhejiang 325035, China
3School of Life and Environmental Science, Wenzhou University, Wenzhou, Zhejiang 325035, China

Received 1 April 2015; Accepted 16 June 2015

Academic Editor: Luca Gori

Copyright © 2015 Yi Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. Rietkerk and J. van de Koppel, “Regular pattern formation in real ecosystems,” Trends in Ecology & Evolution, vol. 23, no. 3, pp. 169–175, 2008. View at Publisher · View at Google Scholar · View at Scopus
  2. M. Scheffer, S. Carpenter, J. A. Foley, C. Folke, and B. Walker, “Catastrophic shifts in ecosystems,” Nature, vol. 413, no. 6856, pp. 591–596, 2001. View at Publisher · View at Google Scholar · View at Scopus
  3. S. Kéfi, M. Rietkerk, C. L. Alados et al., “Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems,” Nature, vol. 449, no. 7159, pp. 213–217, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. M. Rietkerk, S. C. Dekker, P. C. de Ruiter, and J. van de Koppel, “Self-organized patchiness and catastrophic shifts in ecosystems,” Science, vol. 305, no. 5692, pp. 1926–1929, 2004. View at Publisher · View at Google Scholar · View at Scopus
  5. N. Barbier, P. Couteron, J. Lejoly, V. Deblauwe, and O. Lejeune, “Self-organized vegetation patterning as a fingerprint of climate and human impact on semi-arid ecosystems,” Journal of Ecology, vol. 94, no. 3, pp. 537–547, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. J. van de Koppel, D. van der Wal, J. P. Bakker, and P. M. J. Herman, “Self-organization and vegetation collapse in salt marsh ecosystems,” The American Naturalist, vol. 165, no. 1, pp. E1–12, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Rietkerk, M. C. Boerlijst, F. van Langevelde et al., “Self-organization of vegetation in arid ecosystems,” The American Naturalist, vol. 160, no. 4, pp. 524–530, 2002. View at Publisher · View at Google Scholar · View at Scopus
  8. J. van de Koppel and C. M. Crain, “Scale-dependent inhibition drives regular tussock spacing in a freshwater marsh,” The American Naturalist, vol. 168, no. 5, pp. E136–E147, 2006. View at Publisher · View at Google Scholar · View at Scopus
  9. J. van de Koppel, M. Rietkerk, N. Dankers, and P. M. J. Herman, “Scale-dependent feedback and regular spatial patterns in young mussel beds,” The American Naturalist, vol. 165, no. 3, pp. E66–E77, 2005. View at Publisher · View at Google Scholar · View at Scopus
  10. A. B. Rovinsky and M. Menzinger, “Self-organization induced by the differential flow of activator and inhibitor,” Physical Review Letters, vol. 70, no. 6, pp. 778–781, 1993. View at Publisher · View at Google Scholar · View at Scopus
  11. P. Rohani, T. J. Lewis, D. Grünbaum, and G. D. Ruxton, “Spatial self-organisation in ecology: pretty patterns or robust reality?” Trends in Ecology & Evolution, vol. 12, no. 2, pp. 70–74, 1997. View at Publisher · View at Google Scholar · View at Scopus
  12. C. A. Klausmeier, “Regular and irregular patterns in semiarid vegetation,” Science, vol. 284, no. 5421, pp. 1826–1828, 1999. View at Publisher · View at Google Scholar · View at Scopus
  13. R. HilleRisLambers, M. Rietkerk, F. van den Bosch, H. H. T. Prins, and H. de Kroon, “Vegetation pattern formation in semi-arid grazing systems,” Ecology, vol. 82, no. 1, pp. 50–61, 2001. View at Publisher · View at Google Scholar · View at Scopus
  14. Q.-X. Liu, E. J. Weerman, P. M. J. Herman, H. Olff, and J. van de Koppel, “Alternative mechanisms alter the emergent properties of self-organization in mussel beds,” Proceedings of the Royal Society B: Biological Sciences, vol. 279, no. 1739, pp. 2744–2753, 2012. View at Publisher · View at Google Scholar · View at Scopus
  15. O. Lejeune, M. Tlidi, and P. Couteron, “Localized vegetation patches: a self-organized response to resource scarcity,” Physical Review E—Statistical, Nonlinear, and Soft Matter Physics, vol. 66, no. 1, Article ID 010901, 2002. View at Publisher · View at Google Scholar · View at Scopus
  16. S. Mistr and D. Bercovici, “A theoretical model of pattern formation in coral reefs,” Ecosystems, vol. 6, no. 1, pp. 61–74, 2003. View at Publisher · View at Google Scholar · View at Scopus
  17. C. A. Hiemstra, G. E. Liston, and W. A. Reiners, “Snow redistribution by wind and interactions with vegetation at upper treeline in the Medicine Bow Mountains, Wyoming, USA,” Arctic, Antarctic, and Alpine Research, vol. 34, no. 3, pp. 262–273, 2002. View at Publisher · View at Google Scholar · View at Scopus
  18. G. F. Blanchard, D. M. Paterson, L. J. Stal et al., “The effect of geomorphological structures on potential biostabilisation by microphytobenthos on intertidal mudflats,” Continental Shelf Research, vol. 20, no. 10-11, pp. 1243–1256, 2000. View at Publisher · View at Google Scholar · View at Scopus
  19. B. A. Lawrence and J. B. Zedler, “Formation of tussocks by sedges: effects of hydroperiod and nutrients,” Ecological Applications, vol. 21, no. 5, pp. 1745–1759, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. C. J. Dai and M. Zhao, “Nonlinear analysis in a nutrient-algae-zooplankton system with sinking of algae,” Abstract and Applied Analysis, vol. 2014, Article ID 278457, 11 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. Z. M. Yue and W. J. Wang, “Qualitative analysis of a diffusive ratio-dependent Holling-Tanner predator-prey model with Smith growth,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 267173, 9 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  22. R. F. Rao, S. M. Zhong, and X. R. Wang, “Stochastic stability criteria with LMI conditions for Markovian jumping impulsive BAM neural networks with mode-dependent time-varying delays and nonlinear reaction-diffusion,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 1, pp. 258–273, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. Z. Wang, J. Nishihiro, and I. Washitani, “Regeneration of native vascular plants facilitated by Ischaemum aristatum var. glaucum tussocks: an experimental demonstration,” Ecological Research, vol. 27, no. 1, pp. 239–244, 2012. View at Publisher · View at Google Scholar · View at Scopus
  24. B. A. Lawrence, T. J. Fahey, and J. B. Zedler, “Root dynamics of Carex stricta-dominated tussock meadows,” Plant and Soil, vol. 364, no. 1-2, pp. 325–339, 2013. View at Publisher · View at Google Scholar · View at Scopus
  25. C. V. Pao, “On nonlinear reaction-diffusion systems,” Journal of Mathematical Analysis and Applications, vol. 87, no. 1, pp. 165–198, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  26. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, NY, USA, 1992. View at MathSciNet
  27. Y. Lou and W.-M. Ni, “Diffusion, self-diffusion and cross-diffusion,” Journal of Differential Equations, vol. 131, no. 1, pp. 79–131, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. C.-S. Lin, W.-M. Ni, and I. Takagi, “Large amplitude stationary solutions to a chemotaxis system,” Journal of Differential Equations, vol. 72, no. 1, pp. 1–27, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  29. M. X. Wang, “Non-constant positive steady states of the Sel'kov model,” Journal of Differential Equations, vol. 190, no. 2, pp. 600–620, 2003. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. P. Y. Pang and M. X. Wang, “Strategy and stationary pattern in a three-species predator-prey model,” Journal of Differential Equations, vol. 200, no. 2, pp. 245–273, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  31. R. Peng, J. P. Shi, and M. X. Wang, “Stationary pattern of a ratio-dependent food chain model with diffusion,” SIAM Journal on Applied Mathematics, vol. 67, no. 5, pp. 1479–1503, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. W. Y. Chen and M. X. Wang, “Qualitative analysis of predator-prey models with Beddington-DeAngelis functional response and diffusion,” Mathematical and Computer Modelling, vol. 42, no. 1-2, pp. 31–44, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  33. P. Y. Pang and M. Wang, “Qualitative analysis of a ratio-dependent predator-prey system with diffusion,” Proceedings of the Royal Society of Edinburgh—Section A: Mathematics, vol. 133, no. 4, pp. 919–942, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  34. L. Nirenberg, Topics in Nonlinear Functional Analysis, American Mathematical Society (AMS), 1974.
  35. F. Q. Yi, J. J. Wei, and J. P. Shi, “Bifurcation and spatiotemporal patterns in a homogeneous diffusive predator-prey system,” Journal of Differential Equations, vol. 246, no. 5, pp. 1944–1977, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  36. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, CUP Archive, 1981.
  37. A. M. Turing, “The chemical basis of morphogenesis,” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 237, no. 641, pp. 37–72, 1952. View at Publisher · View at Google Scholar
  38. J. A. Sherratt, B. T. Eagan, and M. A. Lewis, “Oscillations and chaos behind predator-prey invasion: mathematical artifact or ecological reality?” Philosophical Transactions of the Royal Society B: Biological Sciences, vol. 352, no. 1349, pp. 21–38, 1997. View at Publisher · View at Google Scholar · View at Scopus
  39. R. M. May, G. R. Conway, M. P. Hassell, and T. R. E. Southwood, “Time delays, density-dependence and single-species oscillations,” The Journal of Animal Ecology, vol. 43, no. 3, pp. 747–770, 1974. View at Publisher · View at Google Scholar
  40. C. M. Crain and M. D. Bertness, “Community impacts of a tussock sedge: is ecosystem engineering important in benign habitats?” Ecology, vol. 86, no. 10, pp. 2695–2704, 2005. View at Publisher · View at Google Scholar · View at Scopus
  41. B. N. Fogel, C. M. Crain, and M. D. Bertness, “Community level engineering effects of Triglochin maritima (seaside arrowgrass) in a salt marsh in northern New England, USA,” Journal of Ecology, vol. 92, no. 4, pp. 589–597, 2004. View at Publisher · View at Google Scholar · View at Scopus
  42. P. Stoll and E. Bergius, “Pattern and process: competition causes regular spacing of individuals within plant populations,” Journal of Ecology, vol. 93, no. 2, pp. 395–403, 2005. View at Publisher · View at Google Scholar · View at Scopus
  43. P. Stoll and D. Prati, “Intraspecific aggregation alters competitive interactions in experimental plant communities,” Ecology, vol. 82, no. 2, pp. 319–327, 2001. View at Publisher · View at Google Scholar · View at Scopus