About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 659152, 6 pages
http://dx.doi.org/10.1155/2014/659152
Research Article

Multiple Periodic Solutions for Discrete Nicholson’s Blowflies Type System

1College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China
2Department of Mathematics, Texas State University, San Marcos, TX 78666, USA

Received 5 January 2014; Accepted 27 February 2014; Published 27 March 2014

Academic Editor: Samir Saker

Copyright © 2014 Hui-Sheng Ding and Julio G. Dix. 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, “An outline of the dynamics of animal populations,” Australian Journal of Zoology, vol. 2, pp. 9–65, 1954.
  2. W. S. Gurney, S. P. Blythe, and R. M. Nisbet, “Nicholson's blowflies revisited,” Nature, vol. 287, pp. 17–21, 1980.
  3. B. Liu, “The existence and uniqueness of positive periodic solutions of Nicholson-type delay systems,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3145–3151, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. W. Chen and L. Wang, “Positive periodic solutions of Nicholson-type delay systems with nonlinear density-dependent mortality terms,” Abstract and Applied Analysis, vol. 2012, Article ID 843178, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Q. Zhou, “The positive periodic solution for Nicholson-type delay system with linear harvesting terms,” Applied Mathematical Modelling: Simulation and Computation for Engineering and Environmental Systems, vol. 37, no. 8, pp. 5581–5590, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. S. H. Saker and S. Agarwal, “Oscillation and global attractivity in a periodic Nicholson's blowflies model,” Mathematical and Computer Modelling, vol. 35, no. 7-8, pp. 719–731, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. 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
  10. J. W.-H. So and J. S. Yu, “On the stability and uniform persistence of a discrete model of Nicholson's blowflies,” Journal of Mathematical Analysis and Applications, vol. 193, no. 1, pp. 233–244, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. J. Alzabut, Y. Bolat, and T. Abdeljawad, “Almost periodic dynamics of a discrete Nicholson's blowflies model involving a linear harvesting term,” Advances in Difference Equations, vol. 2012, article 158, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. O. Alzabut, “Existence and exponential convergence of almost periodic solutions for a discrete Nicholson's blowflies model with a nonlinear harvesting term,” Mathematical Sciences Letters, vol. 2, pp. 201–207, 2013.
  13. S. Padhi, C. Qian, and S. Srivastava, “Multiple periodic solutions for a first order nonlinear functional differential equation with applications to population dynamics,” Communications in Applied Analysis, vol. 12, no. 3, pp. 341–351, 2008. View at Zentralblatt MATH · View at MathSciNet
  14. S. Padhi, S. Srivastava, and J. G. Dix, “Existence of three nonnegative periodic solutions for functional differential equations and applications to hematopoiesis,” Panamerican Mathematical Journal, vol. 19, no. 1, pp. 27–36, 2009. View at Zentralblatt MATH · View at MathSciNet
  15. S. Padhi and S. Pati, “Positive periodic solutions for a nonlinear functional differential equation,” Georgian Academy of Sciences A. Razmadze Mathematical Institute: Memoirs on Differential Equations and Mathematical Physics, vol. 51, pp. 109–118, 2010. View at Zentralblatt MATH · View at MathSciNet
  16. J. O. Alzabut, “Almost periodic solutions for an impulsive delay Nicholson's blowflies model,” Journal of Computational and Applied Mathematics, vol. 234, no. 1, pp. 233–239, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. H.-S. Ding and J. J. Nieto, “A new approach for positive almost periodic solutions to a class of Nicholson's blowflies model,” Journal of Computational and Applied Mathematics, vol. 253, pp. 249–254, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. R. W. Leggett and L. R. Williams, “Multiple positive fixed points of nonlinear operators on ordered Banach spaces,” Indiana University Mathematics Journal, vol. 28, no. 4, pp. 673–688, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. J. G. Dix, S. Padhi, and S. Pati, “Multiple positive periodic solutions for a nonlinear first order functional difference equation,” Journal of Difference Equations and Applications, vol. 16, no. 9, pp. 1037–1046, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. Y. N. Raffoul, “Positive periodic solutions of nonlinear functional difference equations,” Electronic Journal of Differential Equations, no. 55, pp. 1–8, 2002. View at Zentralblatt MATH · View at MathSciNet
  21. Y. N. Raffoul and C. C. Tisdell, “Positive periodic solutions of functional discrete systems and population models,” Advances in Difference Equations, no. 3, pp. 369–380, 2005. View at Zentralblatt MATH · View at MathSciNet
  22. M. N. Islam and Y. N. Raffoul, “Periodic solutions of neutral nonlinear system of differential equations with functional delay,” Journal of Mathematical Analysis and Applications, vol. 331, no. 2, pp. 1175–1186, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. D. Jiang, J. Wei, and B. Zhang, “Positive periodic solutions of functional differential equations and population models,” Electronic Journal of Differential Equations, no. 71, pp. 1–13, 2002. View at Zentralblatt MATH · View at MathSciNet
  24. Z. Zeng, L. Bi, and M. Fan, “Existence of multiple positive periodic solutions for functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 325, no. 2, pp. 1378–1389, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. W. Zhang, D. Zhu, and P. Bi, “Existence of periodic solutions of a scalar functional differential equation via a fixed point theorem,” Mathematical and Computer Modelling, vol. 46, no. 5-6, pp. 718–729, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet