- About this Journal
- Abstracting and Indexing
- 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
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 921879, 12 pages
Pattern Dynamics in a Spatial Predator-Prey System with Allee Effect
1Complex Sciences Center, Shanxi University, Taiyuan, Shan’xi 030006, China
2School of Mathematical Sciences, Shanxi University, Taiyuan, Shan’xi 030006, China
3Institute of Information Economy, Hangzhou Normal University, Hangzhou 310036, China
4Department of Mathematics, North University of China, Taiyuan, Shan’xi 030051, China
5Department of Mathematics, Taiyuan Institute of Technology, Taiyuan, Shan’xi 030008, China
6Web Sciences Center, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
Received 9 May 2013; Accepted 22 August 2013
Academic Editor: Rasajit Bera
Copyright © 2013 Gui-Quan Sun 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.
- W. C. Allee, Animal Aggregations, University of Chicago Press, 1931.
- W. C. Allee and E. Bowen, “Studies in animal aggregations: mass protection against colloidalsilver among goldfishes,” Journal of Experimental Zoology, vol. 61, pp. 185–207, 1932.
- W. C. Allee, O. Emerson, T. Park, and K. Schmidt, Principles of Animal Ecology, Saunders, Philadelphia, Pa, USA, 1949.
- W. C. Allee, Cooperation Among Animals, Henry Shuman, 1951.
- W. C. Allee, The Social Life of Animals, Beacon Press, 1958.
- F. Courchamp, T. Clutton-Brock, and B. Grenfell, “Inverse density dependence and the Allee effect,” Trends in Ecology and Evolution, vol. 14, no. 10, pp. 405–410, 1999.
- P. A. Stephens and W. J. Sutherland, “Consequences of the Allee effect for behaviour, ecology and conservation,” Trends in Ecology and Evolution, vol. 14, no. 10, pp. 401–405, 1999.
- J. Cushing and J. T. Hudson, “Evolutionary dynamics and strong allee effects,” Journal of Biological Dynamics, vol. 6, pp. 941–958, 2012.
- S. N. Elaydi and R. J. Sacker, “Population models with Allee effect: a new model,” Journal of Biological Dynamics, vol. 4, no. 4, pp. 397–408, 2010.
- J. Shi and R. Shivaji, “Persistence in reaction diffusion models with weak Allee effect,” Journal of Mathematical Biology, vol. 52, no. 6, pp. 807–829, 2006.
- J. Wang, J. Shi, and J. Wei, “Predator-prey system with strong Allee effect in prey,” Journal of Mathematical Biology, vol. 62, no. 3, pp. 291–331, 2011.
- A. Verdy, “Modulation of predator-prey interactions by the Allee effect,” Ecological Modelling, vol. 221, no. 8, pp. 1098–1107, 2010.
- V. Méndez, C. Sans, I. Llopis, and D. Campos, “Extinction conditions for isolated populations with Allee effect,” Mathematical Biosciences, vol. 232, no. 1, pp. 78–86, 2011.
- S. V. Petrovskii, A. Y. Morozov, and E. Venturino, “Allee effect makes possible patchy invasion in a predator-prey system,” Ecology Letters, vol. 5, no. 3, pp. 345–352, 2002.
- A. Morozov, S. Petrovskii, and B.-L. Li, “Bifurcations and chaos in a predator-prey system with the Allee effect,” Proceedings of the Royal Society B, vol. 271, no. 1546, pp. 1407–1414, 2004.
- A. Morozov, S. Petrovskii, and B.-L. Li, “Spatiotemporal complexity of patchy invasion in a predator-prey system with the Allee effect,” Journal of Theoretical Biology, vol. 238, no. 1, pp. 18–35, 2006.
- G. H. Gunaratne, Q. Ouyang, and H. L. Swinney, “Pattern formation in the presence of symmetries,” Physical Review E, vol. 50, no. 4, pp. 2802–2820, 1994.
- B. Peña and C. Pérez-García, “Stability of Turing patterns in the Brusselator model,” Physical Review E, vol. 64, no. 5, part 2, Article ID 056213, 9 pages, 2001.
- J. A. Sherratt, “Periodic travelling waves in cyclic predator-prey systems,” Ecology Letters, vol. 4, no. 1, pp. 30–37, 2001.
- M. Baurmann, T. Gross, and U. Feudel, “Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations,” Journal of Theoretical Biology, vol. 245, no. 2, pp. 220–229, 2007.
- M. A. Lewis and P. Kareiva, “Allee dynamics and the spread of invading organisms,” Theoretical Population Biology, vol. 43, no. 2, pp. 141–158, 1993.
- A. M. Turing, “The chemical basis of morphogenesis,” Philosophical Transactions of the Royal Society B, vol. 237, pp. 37–72, 1952.
- Q. Ouyang, Pattern Formation in Reaction-Diffusion Systems, Sci-Tech Education Publishing House, Shanghai, China, 2000.
- F. Courchamp, J. Berec, and J. Gascoigne, Allee Effects in Ecology and Conservation, Oxford University Press, New York, NY, USA, 2008.
- J. D. M. Rademacher, B. Sandstede, and A. Scheel, “Computing absolute and essential spectra using continuation,” Physica D, vol. 229, no. 2, pp. 166–183, 2007.
- P. Wheeler and D. Barkley, “Computation of spiral spectra,” SIAM Journal on Applied Dynamical Systems, vol. 5, no. 1, pp. 157–177, 2006.
- M. Pascual, “Diffusion-induced chaos in a spatial predator-prey system,” Proceedings of the Royal Society B, vol. 251, no. 1330, pp. 1–7, 1993.
- J. A. Sherratt, M. J. Smith, and J. D. M. Rademacher, “Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 27, pp. 10890–10895, 2009.
- M. P. Hassell, J. H. Lawton, and R. M. May, “Patterns of dynamical behaviour in single-species populations,” Journal of Animal Ecology, vol. 45, pp. 471–486, 1976.
- A. A. Berryman and J. A. Millstein, “Are ecological systems chaotic—and if not, why not?” Trends in Ecology and Evolution, vol. 4, no. 1, pp. 26–28, 1989.