Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2011, Article ID 518719, 16 pages
http://dx.doi.org/10.1155/2011/518719
Research Article

Analysis on a Stochastic Predator-Prey Model with Modified Leslie-Gower Response

1Department of Mathematics, Harbin Institute of Technology, Weihai 264209, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received 30 October 2010; Accepted 30 March 2011

Academic Editor: Wing-Sum Cheung

Copyright © 2011 Jingliang Lv and Ke 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.

Linked References

  1. P. H. Leslie, “Some further notes on the use of matrices in population mathematics,” Biometrika, vol. 35, pp. 213–245, 1948. View at Google Scholar
  2. 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 Google Scholar
  3. H. W. Broer, K. Saleh, V. Naudot, and R. Roussarie, “Dynamics of a predator-prey model with non-monotonic response function,” Discrete and Continuous Dynamical Systems, vol. 18, no. 2-3, pp. 221–251, 2007. View at Google Scholar · View at Scopus
  4. M. A. Aziz-Alaoui and M. Daher Okiye, “Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes,” Applied Mathematics Letters, vol. 16, no. 7, pp. 1069–1075, 2003. View at Publisher · View at Google Scholar · View at Scopus
  5. S. B. Hsu and T. W. Huang, “Global stability for a class of predator-prey systems,” SIAM Journal on Applied Mathematics, vol. 55, no. 3, pp. 763–783, 1995. View at Google Scholar · View at Scopus
  6. L. Ji and C. Wu, “limit cycles of a holling-tanner model with modified Leslie-Gower,” Journal of Fuzhou University, vol. 37, pp. 771–797, 2009. View at Google Scholar
  7. 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 Scopus
  8. C. Ji, D. Jiang, and X. Li, “Qualitative analysis of a stochastic ratio-dependent predatorprey system,” Journal of Computational and Applied Mathematics, vol. 235, no. 5, pp. 1326–1341, 2011. View at Publisher · View at Google Scholar
  9. X. Mao, G. Marion, and E. Renshaw, “Environmental Brownian noise suppresses explosions in population dynamics,” Stochastic Processes and Their Applications, vol. 97, no. 1, pp. 95–110, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. X. Y. Li and X. Mao, “Population dynamical behavior of non-autonomous lotka-volterra competitive system with random perturbation,” Discrete and Continuous Dynamical Systems, vol. 24, no. 2, pp. 523–545, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Chen and J. Chen, Nonlinear Biological Dynamical System, Science Press, Beijing, China, 1993.