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Journal of Applied Mathematics
Volume 2014, Article ID 431671, 10 pages
http://dx.doi.org/10.1155/2014/431671
Research Article

Global Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure

1School of Mathematics and Statistics, Hebei University of Economics & Business, Shijiazhuang 050061, China
2Department of Basic Courses, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 10 June 2013; Accepted 6 January 2014; Published 25 February 2014

Academic Editor: Keshlan S. Govinder

Copyright © 2014 Lingshu Wang and Guanghui Feng. 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. Y. Kuang and J. W.-H. So, “Analysis of a delayed two-stage population model with space-limited recruitment,” SIAM Journal on Applied Mathematics, vol. 55, no. 6, pp. 1675–1696, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. W. Wang, “Global dynamics of a population model with stage structure for predator,” in Advanced Topics in Biomathematics, L. Chen, S. Ruan, and J. Zhu, Eds., pp. 253–257, Word Scientific Publishing, 1997. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. Wang and L. Chen, “A predator-prey system with stage-structure for predator,” Computers & Mathematics with Applications, vol. 33, no. 8, pp. 83–91, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  4. Y. N. Xiao and L. S. Chen, “Global stability of a predator-prey system with stage structure for the predator,” Acta Mathematica Sinica, vol. 20, no. 1, pp. 63–70, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. R. Xu, “Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response,” Nonlinear Dynamics, vol. 67, no. 2, pp. 1683–1693, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. R. Xu, “Global dynamics of a predator-prey model with time delay and stage structure for the prey,” Nonlinear Analysis. Real World Applications, vol. 12, no. 4, pp. 2151–2162, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. C. S. Holling, “The functional response of predators to prey density and its role in minicry and population regulation,” Memoirs of the Entomological Society of Canada, vol. 45, pp. 3–60, 1965. View at Google Scholar
  8. Y. Kuang, Delay Differential Equation with Application in Population Synamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1993. View at MathSciNet
  9. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1981. View at MathSciNet
  10. J. Hale, Theory of Functional Differential Equation, Springer, Heidelberg, Germany, 1977. View at MathSciNet
  11. J. K. Hale and P. Waltman, “Persistence in infinite-dimensional systems,” SIAM Journal on Mathematical Analysis, vol. 20, no. 2, pp. 388–395, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet