- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 218053, 7 pages
Rich Spatiotemporal Dynamics of a Vegetation Model with Noise and Periodic Forcing
1National Key Laboratory for Electronic Measurement Technology, North University of China, Taiyuan, Shanxi 030051, China
2Key Laboratory of Instrumentation Science and Dynamic Measurement, Ministry of Education, North University of China, Taiyuan, Shanxi 030051, China
Received 1 September 2013; Revised 16 December 2013; Accepted 4 January 2014; Published 3 March 2014
Academic Editor: Ryusuke Kon
Copyright © 2014 Xia-Xia Zhao and Jian-Zhong Wang. 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.
- M. Scheffer, A. H. Bakema, and F. G. Wolterboer, “MEGAPLANT: a simulation model of the dynamics of submerged plants,” Aquatic Botany, vol. 45, no. 4, pp. 341–356, 1993.
- B. T. Grenfell, B. M. Bolker, and A. Kleczkowski, “Seasonality and extinction in chaotic metapopulations,” Proceedings of the Royal Society B, vol. 259, no. 1354, pp. 97–103, 1995.
- A. A. King and W. M. Schaffer, “The geometry of a population cycle: a mechanistic model of snowshoe hare demography,” Ecology, vol. 82, no. 3, pp. 814–830, 2001.
- S. Altizer, A. Dobson, P. Hosseini, P. Hudson, M. Pascual, and P. Rohani, “Seasonality and the dynamics of infectious diseases,” Ecology Letters, vol. 9, no. 4, pp. 467–484, 2006.
- V. Guttal and C. Jayaprakash, “Self-organization and productivity in semi-arid ecosystems: implications of seasonality in rainfall,” Journal of Theoretical Biology, vol. 248, no. 3, pp. 490–500, 2007.
- A. Provata, I. M. Sokolov, and B. Spagnolo, “Editorial: ecological complex systems,” European Physical Journal B, vol. 65, no. 3, pp. 307–314, 2008.
- O. Richter, “Spatio-temporal patterns of gene flow and dispersal under temperature increase,” Mathematical Biosciences, vol. 218, no. 1, pp. 15–23, 2009.
- G. Q. Sun, Z. Jin, L. Li, and Q. X. Liu, “The role of noise in a predator-prey model with Allee effect,” Journal of Biological Physics, vol. 35, pp. 185–196, 2009.
- G.-Q. Sun, L. Li, Z. Jin, and B.-L. Li, “Effect of noise on the pattern formation in an epidemic model,” Numerical Methods for Partial Differential Equations, vol. 26, no. 5, pp. 1168–1179, 2010.
- J. G. Vilar and R. V. Sole, “Effects of noise in symmetric two-species competition,” Physical Review Letters, vol. 80, pp. 4099–4102, 1998.
- Q. X. Liu and Z. Jin, “Resonance and frequency-locking phenomena in spatially extended phytoplankton–zooplankton system with additive noise and periodic forces,” Journal of Statistical Mechanics, vol. 5, Article ID P05011, 2008.
- F. Rao, W. Wang, and Z. Li, “Spatiotemporal complexity of a predator-prey system with the effect of noise and external forcing,” Chaos, Solitons & Fractals, vol. 41, no. 4, pp. 1634–1644, 2009.
- G.-Q. Sun, Z. Jin, Q.-X. Liu, and B.-L. Li, “Rich dynamics in a predator-prey model with both noise and periodic force,” BioSystems, vol. 100, no. 1, pp. 14–22, 2010.
- O. Lejeune, M. Tlidi, and P. Couteron, “Localized vegetation patches: a self-organized response to resource scarcity,” Physical Review E, vol. 66, no. 1, Article ID 010901, 2002.
- S. B. Boaler and C. A. H. Hodge, “Vegetation stripes in Somaliland,” Journal of Ecology, vol. 50, pp. 465–474, 1962.
- F. T. Maestre and J. Cortina, “Spatial patterns of surface soil properties and vegetation in a Mediterranean semi-arid steppe,” Plant and Soil, vol. 241, no. 2, pp. 279–291, 2002.
- C. A. Klausmeier, “Regular and irregular patterns in semiarid vegetation,” Science, vol. 284, no. 5421, pp. 1826–1828, 1999.
- 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.
- M. Rietkerk and J. van de Koppel, “Regular pattern formation in real ecosystems,” Trends in Ecology and Evolution, vol. 23, no. 3, pp. 169–175, 2008.
- C. Valentin, J. M. D'Herbès, and J. Poesen, “Soil and water components of banded vegetation patterns,” Catena, vol. 37, no. 1-2, pp. 1–24, 1999.
- J. Von Hardenberg, E. Meron, M. Shachak, and Y. Zarmi, “Diversity of vegetation patterns and desertification,” Physical Review Letters, vol. 87, no. 19, Article ID 198101, 2001.
- K. L. Kirk and J. J. Gilbert, “Variation in herbivore response to chemical defenses: zooplankton foraging on toxic cyanobacteria,” Ecology, vol. 73, no. 6, pp. 2208–2217, 1992.
- T. Reichenbach, M. Mobilia, and E. Frey, “Noise and correlations in a spatial population model with cyclic competition,” Physical Review Letters, vol. 99, no. 23, Article ID 238105, 2007.
- T. Reichenbach, M. Mobilia, and E. Frey, “Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games,” Nature, vol. 448, no. 7157, pp. 1046–1049, 2007.
- R. Mankin, A. Ainsaar, A. Haljas, and E. Reiter, “Trichotomous-noise-induced catastrophic shifts in symbiotic ecosystems,” Physical Review E, vol. 65, no. 5, Article ID 051108, 2002.
- R. Mankin, A. Sauga, A. Ainsaar, A. Haljas, and K. Paunel, “Colored-noise-induced discontinuous transitions in symbiotic ecosystems,” Physical Review E, vol. 69, no. 6, Article ID 061106, 2004.
- D. J. Higham, “An algorithmic introduction to numerical simulation of stochastic differential equations,” SIAM Review, vol. 43, no. 3, pp. 525–546, 2001.
- G. Q. Sun, Z. Jin, Q. X. Liu, and L. Li, “Dynamical complexity of a spatial predator–prey model with migration,” Ecological Modelling, vol. 219, pp. 248–255, 2008.
- G. Q. Sun, L. Li, Z. Jin, and B. L. Li, “Pattern formation in a spatial plant-wrack model with tide effect on the wrack,” Journal of Biological Physics, vol. 36, pp. 161–174, 2010.
- G.-Q. Sun, J. Li, B. Yu, and Z. Jin, “Noise induced pattern transition in a vegetation model,” Applied Mathematics and Computation, vol. 221, pp. 463–468, 2013.
- C. Zimmer, “Life after chaos,” Science, vol. 284, pp. 83–86, 1999.
- B. Blasius, A. Huppert, and L. Stone, “Complex dynamics and phase synchronization in spatially extended ecological systems,” Nature, vol. 399, no. 6734, pp. 354–359, 1999.
- F. N. Si, Q. X. Liu, J. Z. Zhang, and L. Q. Zhou, “Propagation of travelling waves in sub-excitable systems driven by noise and periodic forcing,” The European Physical Journal B, vol. 60, pp. 507–513, 2007.
- P. D'Odorico, F. Laio, and L. Ridolfi, “Noise-induced stability in dryland plant ecosystems,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, pp. 10819–10822, 2005.
- P. D’Odorico, A. Porporato, and L. Ridolfi, “Transition between stable states in the dynamics of soil development,” Geophysical Research Letters, vol. 28, pp. 595–598, 2001.
- V. Isham, D. R. Cox, I. Rodríguez-Iturbe, A. Porporato, and S. Manfreda, “Representation of space-time variability of soil moisture,” Proceedings of the Royal Society A, vol. 461, no. 2064, pp. 4035–4055, 2005.
- M. Fras and M. Gosak, “Spatiotemporal patterns provoked by environmental variability in a predator–prey model,” Biosystems, vol. 114, pp. 172–177, 2013.
- L. Ridolfi, P. D'Odorico, and F. Laio, “Vegetation dynamics induced by phreatophyte-aquifer interactions,” Journal of Theoretical Biology, vol. 248, no. 2, pp. 301–310, 2007.
- D. Tilman, Dynamics and Structure of Plant Communities, Princeton University Press, Princeton, NJ, USA, 1988.
- J. P. Grover, Resource Competition, Chapman and Hall, New York, NY, USA, 1997.