Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2006, Article ID 31614, 10 pages
http://dx.doi.org/10.1155/DDNS/2006/31614

Global attractivity of positive periodic solutions for an impulsive delay periodic “food limited” population model

College of Network Education, Lanzhou University of Technology, Lanzhou 730050, Gansu, China

Received 14 February 2006; Accepted 16 May 2006

Copyright © 2006 Jian Song. 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. D. D. Baĭnov and P. S. Simeonov, Systems with Impulse Effect. Stability, Theory and Applications, Ellis Horwood Series: Mathematics and Its Applications, Ellis Horwood, Chichester, 1989. View at Zentralblatt MATH · View at MathSciNet
  2. G. Ballinger and X. Liu, “Existence and uniqueness results for impulsive delay differential equations,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 5, no. 1–4, pp. 579–591, 1999. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, vol. 74 of Mathematics and Its Applications, Kluwer Academic, Dordrecht, 1992. View at Zentralblatt MATH · View at MathSciNet
  4. K. Gopalsamy, M. R. S. Kulenović, and G. Ladas, “Oscillations and global attractivity in respiratory dynamics,” Dynamics and Stability of Systems, vol. 4, no. 2, pp. 131–139, 1989. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K. Gopalsamy and B. G. Zhang, “On delay differential equations with impulses,” Journal of Mathematical Analysis and Applications, vol. 139, no. 1, pp. 110–122, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. F. Huo and W. T. Li, “Global attractivity and oscillation in a periodic “food-limited” population model with delay,” Acta Mathematica Scientia, vol. 25, no. 2, pp. 158–165, 2005. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191 of Mathematics in Science and Engineering, Academic Press, Massachusetts, 1993. View at Zentralblatt MATH · View at MathSciNet
  8. G. Ladas, Y. G. Sficas, and I. P. Stavroulakis, “Asymptotic behavior of solutions of retarded differential equations,” Proceedings of the American Mathematical Society, vol. 88, no. 2, pp. 247–253, 1983. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, New Jersey, 1989. View at Zentralblatt MATH · View at MathSciNet
  10. X. Liu and G. Ballinger, “Uniform asymptotic stability of impulsive delay differential equations,” Computers & Mathematics with Applications, vol. 41, no. 7-8, pp. 903–915, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. X. Liu and G. Ballinger, “Existence and continuability of solutions for differential equations with delays and state-dependent impulses,” Nonlinear Analysis. Theory, Methods & Applications, vol. 51, no. 4, pp. 633–647, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. X. Liu and G. Ballinger, “Boundedness for impulsive delay differential equations and applications to population growth models,” Nonlinear Analysis. Theory, Methods & Applications, vol. 53, no. 7-8, pp. 1041–1062, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. S. G. Pandit, “On the stability of impulsively perturbed differential systems,” Bulletin of the Australian Mathematical Society, vol. 17, no. 3, pp. 423–432, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. G. Roberts and R. R. Kao, “The dynamics of an infectious disease in a population with birth pulses,” Mathematical Biosciences, vol. 149, no. 1, pp. 23–36, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. J. H. Shen, “Global existence and uniqueness, oscillation, and nonoscillation of impulsive delay differential equations,” Acta Mathematica Sinica, vol. 40, no. 1, pp. 53–59, 1997 (Chinese). View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. Yan, “Existence and global attractivity of positive periodic solution for an impulsive Lasota-Wazewska model,” Journal of Mathematical Analysis and Applications, vol. 279, no. 1, pp. 111–120, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet