- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 302065, 15 pages
Exponential Extinction of Nicholson's Blowflies System with Nonlinear Density-Dependent Mortality Terms
College of Mathematics, Physics and Information Engineering, Jiaxing University, Jiaxing 314001, China
Received 17 September 2012; Revised 7 December 2012; Accepted 10 December 2012
Academic Editor: Juntao Sun
Copyright © 2012 Wentao 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, “The self adjustment of population to change,” Cold Spring Harbor Symposia on Quantitative Biology, vol. 22, pp. 153–173, 1957.
- W. S. C. Gurney, S. P. Blythe, and R. M. Nisbet, “Nicholson's blowflies revisited,” Nature, vol. 287, pp. 17–21, 1980.
- B. Liu, “Global stability of a class of Nicholson's blowflies model with patch structure and multiple time-varying delays,” Nonlinear Analysis: Real World Applications, vol. 11, no. 4, pp. 2557–2562, 2010.
- 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. 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.
- M. Li and J. Yan, “Oscillation and global attractivity of generalized Nicholson's blowfly model,” in Differential Equations and Computational Simulations, pp. 196–201, World Scientific, River Edge, NJ, USA, 2000.
- Y. Chen, “Periodic solutions of delayed periodic Nicholson's blowflies models,” The Canadian Applied Mathematics Quarterly, vol. 11, no. 1, pp. 23–28, 2003.
- J. Li and C. Du, “Existence of positive periodic solutions for a generalized Nicholson's blowflies model,” Journal of Computational and Applied Mathematics, vol. 221, no. 1, pp. 226–233, 2008.
- 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.
- W. Wang, “Positive periodic solutions of delayed Nicholson's blowflies models with a nonlinear density-dependent mortality term,” Applied Mathematical Modelling, vol. 36, no. 10, pp. 4708–4713, 2012.
- X. Hou, L. Duan, and Z. Huang, “Permanence and periodic solutions for a class of delay Nicholson's blowflies models,” Applied Mathematical Modelling, vol. 37, no. 3, pp. 1537–1544, 2012.
- B. Liu and S. Gong, “Permanence for Nicholson-type delay systems with nonlinear density-dependent mortality terms,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 1931–1937, 2011.
- Y. Takeuchi, W. Wang, and Y. Saito, “Global stability of population models with patch structure,” Nonlinear Analysis: Real World Applications, vol. 7, no. 2, pp. 235–247, 2006.
- T. Faria, “Global asymptotic behaviour for a Nicholson model with patch structure and multiple delays,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 18, pp. 7033–7046, 2011.
- B. Liu, “Global stability of a class of delay differential systems,” Journal of Computational and Applied Mathematics, vol. 233, no. 2, pp. 217–223, 2009.
- L. Berezansky, L. Idels, and L. Troib, “Global dynamics of Nicholson-type delay systems with applications,” Nonlinear Analysis: Real World Applications, vol. 12, no. 1, pp. 436–445, 2011.
- H. L. Smith, Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative System, vol. 41 of Mathematical Surveys and Monographs, American Mathematical Society, Providence, RI, USA, 1995.
- J. K. Hale and S. M. Verduyn Lunel, Introduction to Functional-Differential Equations, vol. 99 of Applied Mathematical Sciences, Springer, New York, NY, USA, 1993.