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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 101764, 6 pages
http://dx.doi.org/10.1155/2013/101764
Research Article

Global Attractivity of a Diffusive Nicholson's Blowflies Equation with Multiple Delays

Department of Mathematics and System Science, College of Science, National University of Defense Technology, Changsha 410073, China

Received 29 January 2013; Accepted 3 April 2013

Academic Editor: Chuangxia Huang

Copyright © 2013 Xiongwei Liu and Xiao 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. A. J. Nicholson, “Competition for food amongst Lucilia Cuprina larvae,” in Proceedings of the 8th International Congress of Entomology, vol. 15, pp. 277–281, Stockholm, Sweden, 1948.
  2. A. J. Nicholson, “An outline of the dynamics of animal populations,” Australian Journal of Zoology, vol. 2, pp. 9–65, 1954.
  3. W. S. C. Gurney, S. P. Blythe, and R. M. Nisbet, “Nicholson's blowflies revisited,” Nature, vol. 287, pp. 17–21, 1980. View at Publisher · View at Google Scholar
  4. L. Berezansky, E. Braverman, and L. Idels, “Nicholson's blowflies differential equations revisited: main results and open problems,” Applied Mathematical Modelling, vol. 34, no. 6, pp. 1405–1417, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. Karakostas, C. G. Philos, and Y. G. Sficas, “Stable steady state of some population models,” Journal of Dynamics and Differential Equations, vol. 4, no. 1, pp. 161–190, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. M. R. S. Kulenović and G. Ladas, “Linearized oscillations in population dynamics,” Bulletin of Mathematical Biology, vol. 49, no. 5, pp. 615–627, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M. R. S. Kulenović, G. Ladas, and Y. G. Sficas, “Global attractivity in Nicholson's blowflies,” Applicable Analysis, vol. 43, no. 1-2, pp. 109–124, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. J. Li, “Global attractivity in Nicholson's blowflies,” Applied Mathematics B, vol. 11, no. 4, pp. 425–434, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. W.-H. So and J. S. Yu, “Global attractivity and uniform persistence in Nicholson's blowflies,” Differential Equations and Dynamical Systems, vol. 2, no. 1, pp. 11–18, 1994. View at Zentralblatt MATH · View at MathSciNet
  10. Y. Yang and J. W. H. So, “Dynamics for the diffusive Nicholson blowflies equation,” in Proceedings of the International Conference on Dynamical Systems and Differential Equations, vol. II, Springfield, USA, 1996.
  11. C.-K. Lin and M. Mei, “On travelling wavefronts of Nicholson's blowflies equation with diffusion,” Proceedings of the Royal Society of Edinburgh A, vol. 140, no. 1, pp. 135–152, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. H. Saker, “Oscillation of continuous and discrete diffusive delay Nicholson's blowflies models,” Applied Mathematics and Computation, vol. 167, no. 1, pp. 179–197, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. X. Wang and Z. Li, “Dynamics for a type of general reaction-diffusion model,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 67, no. 9, pp. 2699–2711, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. T. Yi and X. Zou, “Global attractivity of the diffusive Nicholson blowflies equation with Neumann boundary condition: a non-monotone case,” Journal of Differential Equations, vol. 245, no. 11, pp. 3376–3388, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations and Applications, Clarendon Press, New York, NY, USA, 1991.
  16. J. W. Luo and K. Y. Liu, “Global attractivity of a generalized Nicholson blowfly model,” Hunan Daxue Xuebao, vol. 23, no. 4, pp. 13–17, 1996. View at MathSciNet
  17. X. Wang and Z. X. Li, “Oscillations for a diffusive Nicholson blowflies equation with several arguments,” Applied Mathematics A, vol. 20, no. 3, pp. 265–274, 2005. View at Zentralblatt MATH · View at MathSciNet
  18. R. Redlinger, “On Volterra's population equation with diffusion,” SIAM Journal on Mathematical Analysis, vol. 16, no. 1, pp. 135–142, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. R. Redlinger, “Existence theorems for semilinear parabolic systems with functionals,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 8, no. 6, pp. 667–682, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. W.-H. So, J. Wu, and Y. Yang, “Numerical steady state and Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation,” Applied Mathematics and Computation, vol. 111, no. 1, pp. 33–51, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet