About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401031, 24 pages
http://dx.doi.org/10.1155/2012/401031
Research Article

The Complex Dynamics of a Stochastic Predator-Prey Model

1College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China
2School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China

Received 19 May 2012; Accepted 29 July 2012

Academic Editor: Sergey V. Zelik

Copyright © 2012 Xixi 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. H. I. Freedman, Deterministic Mathematical Models in Population Ecology, Marcel Dekker, New York, NY, USA, 1980. View at Zentralblatt MATH
  2. P. H. Leslie, “Some further notes on the use of matrices in population mathematics,” Biometrika, vol. 35, no. 3-4, pp. 213–245, 1948. View at Zentralblatt MATH
  3. P. H. Leslie, “A stochastic model for studying the properties of certain biological systems by numerical methods,” Biometrika, vol. 45, pp. 16–31, 1958. View at Zentralblatt MATH
  4. H.-F. Huo and W.-T. Li, “Stable periodic solution of the discrete periodic Leslie-Gower predator-prey model,” Mathematical and Computer Modelling, vol. 40, no. 3-4, pp. 261–269, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. H.-F. Huo and W.-T. Li, “Periodic solutions of delayed Leslie-Gower predator-prey models,” Applied Mathematics and Computation, vol. 155, no. 3, pp. 591–605, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. F. Chen, “Permanence in nonautonomous multi-species predator-prey system with feedback controls,” Applied Mathematics and Computation, vol. 173, no. 2, pp. 694–709, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. F. Chen and X. Cao, “Existence of almost periodic solution in a ratio-dependent Leslie system with feedback controls,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 1399–1412, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. C. Ji, D. Jiang, and N. Shi, “Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with stochastic perturbation,” Journal of Mathematical Analysis and Applications, vol. 359, no. 2, pp. 482–498, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. M. Liu and K. Wang, “Global stability of a nonlinear stochastic predator-prey system with Beddington-DeAngelis functional response,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1114–1121, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. T. C. Gard, “Persistence in stochastic food web models,” Bulletin of Mathematical Biology, vol. 46, no. 3, pp. 357–370, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. T. C. Gard, “Stability for multispecies population models in random environments,” Nonlinear Analysis. Theory, Methods & Applications, vol. 10, no. 12, pp. 1411–1419, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. R. M. May, Stability and Complexity in Model Ecosystems, vol. 6, Princeton University Press, 2001.
  13. X. Mao, Stochastic Differential Equations and Their Applications, Horwood Publishing Limited, 1997.
  14. Q. Luo and X. Mao, “Stochastic population dynamics under regime switching,” Journal of Mathematical Analysis and Applications, vol. 334, no. 1, pp. 69–84, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. X. Mao, C. Yuan, and J. Zou, “Stochastic differential delay equations of population dynamics,” Journal of Mathematical Analysis and Applications, vol. 304, no. 1, pp. 296–320, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. Pang, F. Deng, and X. Mao, “Asymptotic properties of stochastic population dynamics,” Dynamics of Continuous, Discrete & Impulsive Systems A, vol. 15, no. 5, pp. 603–620, 2008. View at Zentralblatt MATH
  17. D. J. Higham, “An algorithmic introduction to numerical simulation of stochastic differential equations,” SIAM Review, vol. 43, no. 3, pp. 525–546, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH