About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 393729, 9 pages
http://dx.doi.org/10.1155/2013/393729
Research Article

Permanence and Global Attractivity of the Discrete Predator-Prey System with Hassell-Varley-Holling III Type Functional Response

Department of Mathematics and Physics, Fujian University of Technology, Fuzhou, Fujian 350108, China

Received 6 November 2012; Revised 18 February 2013; Accepted 19 February 2013

Academic Editor: M. De la Sen

Copyright © 2013 Runxin Wu and Lin Li. 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. R. Wu and L. Li, “Permanence and global attractivity of discrete predator-prey system with hassell-varley type functional response,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 323065, 17 pages, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. H.-F. Huo and W.-T. Li, “Permanence and global stability of positive solutions of a nonautonomous discrete ratio-dependent predator-prey model,” Discrete Dynamics in Nature and Society, no. 2, pp. 135–144, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. J. Yang, “Dynamics behaviors of a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 186539, 19 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. Huang, F. Chen, and L. Zhong, “Stability analysis of a prey-predator model with Holling type III response function incorporating a prey refuge,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 672–683, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. F. Chen, “Permanence and global attractivity of a discrete multispecies Lotka-Volterra competition predator-prey systems,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 3–12, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  6. A. L. Nevai and R. A. Van Gorder, “Effect of resource subsidies on predator-prey population dynamics: a mathematical model,” Journal of Biological Dynamics, vol. 6, no. 2, pp. 891–922, 2012. View at Publisher · View at Google Scholar
  7. M. P. Hassell and G. C. Varley, “New inductive population model for insect parasites and its bearing on biological control,” Nature, vol. 223, no. 5211, pp. 1133–1137, 1969. View at Publisher · View at Google Scholar · View at Scopus
  8. X. X. Liu and L. H. Huang, “Positive periodic solutions for a discrete system with Hassell-Varley type functional response,” Mathematics in Practice and Theory, no. 12, pp. 115–120, 2009.
  9. M. L. Zhong and X. X. Liu, “Dynamical analysis of a predator-prey system with Hassell-Varley-Holling functional response,” Acta Mathematica Scientia. Series A, vol. 31, no. 5, pp. 1295–1310, 2011. View at Zentralblatt MATH · View at MathSciNet
  10. R. Arditi and H. R. Akçakaya, “Underestimation of mutual interference of predators,” Oecologia, vol. 83, no. 3, pp. 358–361, 1990. View at Publisher · View at Google Scholar · View at Scopus
  11. W. J. Sutherland, “Aggregation and the “ideal free” distribution,” Journal of Animal Ecology, vol. 52, no. 3, pp. 821–828, 1983. View at Scopus
  12. D. Schenk, L. F. Bersier, and S. Bacher, “An experimental test of the nature of predation: neither prey- nor ratio-dependent,” Journal of Animal Ecology, vol. 74, no. 1, pp. 86–91, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. S.-B. Hsu, T.-W. Hwang, and Y. Kuang, “Global dynamics of a predator-prey model with Hassell-Varley type functional response,” Discrete and Continuous Dynamical Systems. Series B, vol. 10, no. 4, pp. 857–871, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. F. Chen, “Permanence for the discrete mutualism model with time delays,” Mathematical and Computer Modelling, vol. 47, no. 3-4, pp. 431–435, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. Y.-H. Fan and L.-L. Wang, “Permanence for a discrete model with feedback control and delay,” Discrete Dynamics in Nature and Society, vol. 2008, Article ID 945109, 8 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. F. Chen, “Permanence of a discrete N-species cooperation system with time delays and feedback controls,” Applied Mathematics and Computation, vol. 186, no. 1, pp. 23–29, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Z. Li and F. Chen, “Extinction in two dimensional discrete Lotka-Volterra competitive system with the effect of toxic substances,” Dynamics of Continuous, Discrete & Impulsive Systems. Series B, vol. 15, no. 2, pp. 165–178, 2008. View at Zentralblatt MATH · View at MathSciNet
  18. F. Chen, “Average conditions for permanence and extinction in nonautonomous Gilpin-Ayala competition model,” Nonlinear Analysis: Real World Applications, vol. 7, no. 4, pp. 895–915, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet