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International Journal of Differential Equations
Volume 2017, Article ID 2653124, 11 pages
https://doi.org/10.1155/2017/2653124
Research Article

Analysis of a Predator-Prey Model with Switching and Stage-Structure for Predator

Center of Excellence in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand

Correspondence should be addressed to T. Suebcharoen; moc.liamg@s.hsunareet

Received 8 June 2017; Accepted 22 August 2017; Published 27 September 2017

Academic Editor: Yuji Liu

Copyright © 2017 T. Suebcharoen. 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. C. Celik, “The stability and Hopf bifurcation for a predator-prey system with time delay,” Chaos, Solitons and Fractals, vol. 37, no. 1, pp. 87–99, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  2. H. I. Freedman and S. G. Ruan, “Hopf bifurcation in three-species food chain models with group defense,” Mathematical Biosciences, vol. 111, no. 1, pp. 73–87, 1992. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. 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 Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. S.-B. Hsu and T.-W. Hwang, “Hopf bifurcation analysis for a predator-prey system of Holling and Leslie type,” Taiwanese Journal of Mathematics, vol. 3, no. 1, pp. 35–53, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. Z. Lu and X. Liu, “Analysis of a predator-prey model with modified Holling-Tanner functional response and time delay,” Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 9, no. 2, pp. 641–650, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. Y. Song and S. Yuan, “Bifurcation analysis in a predator-prey system with time delay,” Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 7, no. 2, pp. 265–284, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. Tansky, “Switching effect in prey-predator system,” Journal of Theoretical Biology, vol. 70, no. 3, pp. 263–271, 1978. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Q. J. Khan, E. Balakrishnan, and G. C. Wake, “Analysis of a predator-prey system with predator switching,” Bulletin of Mathematical Biology, vol. 66, no. 1, pp. 109–123, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. W. W. Murdoch, “Switching in general predators: experiments on predator specificity and stability of prey populations,” Ecological Monographs, vol. 39, no. 4, pp. 335–364, 1969. View at Publisher · View at Google Scholar
  10. Prajneshu and P. Holgate, “A prey-predator model with switching effect,” Journal of Theoretical Biology, vol. 125, no. 1, pp. 61–66, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  11. E. Teramoto, K. Kawasaki, and N. Shigesada, “Switching effect of predation on competitive prey species,” Journal of Theoretical Biology, vol. 79, no. 3, pp. 303–315, 1979. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Y. Saito and Y. Takeuchi, “A time-delay model for prey-predator growth with stage structure,” Canadian Applied Mathematics Quarterly, vol. 11, no. 3, pp. 293–302, 2003. View at Google Scholar · View at MathSciNet
  13. W. G. Aiello and H. I. Freedman, “A time-delay model of single-species growth with stage structure,” Mathematical Biosciences, vol. 101, no. 2, pp. 139–153, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. W. G. Aiello, H. I. Freedman, and J. Wu, “Analysis of a model representing stage-structured population growth with state-dependent time delay,” SIAM Journal on Applied Mathematics, vol. 52, no. 3, pp. 855–869, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Y. Qu and J. Wei, “Bifurcation analysis in a time-delay model for prey-predator growth with stage-structure,” Nonlinear Dynamics. An International Journal of Nonlinear Dynamics and Chaos in Engineering Systems, vol. 49, no. 1-2, pp. 285–294, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. M. Y. Li and H. Shu, “Global dynamics of a mathematical model for HTLV-I infection of CD4+T cells with delayed CTL response,” Nonlinear Analysis: Real World Applications, vol. 13, no. 3, pp. 1080–1092, 2012. View at Publisher · View at Google Scholar · View at MathSciNet