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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 101764, 6 pages
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.
- 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.
- A. J. Nicholson, “An outline of the dynamics of animal populations,” Australian Journal of Zoology, vol. 2, pp. 9–65, 1954.
- W. S. C. Gurney, S. P. Blythe, and R. M. Nisbet, “Nicholson's blowflies revisited,” Nature, vol. 287, pp. 17–21, 1980.
- 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.
- 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.
- M. R. S. Kulenović and G. Ladas, “Linearized oscillations in population dynamics,” Bulletin of Mathematical Biology, vol. 49, no. 5, pp. 615–627, 1987.
- 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.
- J. Li, “Global attractivity in Nicholson's blowflies,” Applied Mathematics B, vol. 11, no. 4, pp. 425–434, 1996.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations and Applications, Clarendon Press, New York, NY, USA, 1991.
- 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.
- 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.
- R. Redlinger, “On Volterra's population equation with diffusion,” SIAM Journal on Mathematical Analysis, vol. 16, no. 1, pp. 135–142, 1985.
- R. Redlinger, “Existence theorems for semilinear parabolic systems with functionals,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 8, no. 6, pp. 667–682, 1984.
- 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.