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Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 195983, 11 pages
http://dx.doi.org/10.1155/2010/195983
Research Article

The Permanence in a Single Species Nonautonomous System with Delays and Feedback Control

Department of Mathematics, Yuncheng University, Yuncheng 044000, China

Received 27 October 2009; Accepted 6 January 2010

Academic Editor: Guang Zhang

Copyright © 2010 Xiaomei Feng and Fengqin Zhang. 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. B. G. Zhang and K. Gopalsamy, “Global attractivity and oscillations in a periodic delay-logistic equation,” Journal of Mathematical Analysis and Applications, vol. 150, no. 1, pp. 274–283, 1990. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. Yuan and J. Hong, “The existence of almost periodic solution of a population equation with delay,” Applicable Analysis, vol. 61, no. 1-2, pp. 45–52, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
  3. Z. Teng, “Permanence and stability in non-autonomous logistic systems with infinite delay,” Dynamical Systems, vol. 17, no. 3, pp. 187–202, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Z. Teng, “Persistence and stability in general nonautonomous single-species Kolmogorov systems with delays,” Nonlinear Analysis: Real World Applications, vol. 8, no. 1, pp. 230–248, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. H. I. Freedman and J. H. Wu, “Periodic solutions of single-species models with periodic delay,” SIAM Journal on Mathematical Analysis, vol. 23, no. 3, pp. 689–701, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. Seifert, “On a delay-differential equation for single specie population variations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 11, no. 9, pp. 1051–1059, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  7. K. Gopalsamy and P. X. Weng, “Feedback regulation of logistic growth,” International Journal of Mathematics and Mathematical Sciences, vol. 16, no. 1, pp. 177–192, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. F. Chen, “Positive periodic solutions of neutral Lotka-Volterra system with feedback control,” Applied Mathematics and Computation, vol. 162, no. 3, pp. 1279–1302, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H.-F. Huo and W.-T. Li, “Positive periodic solutions of a class of delay differential system with feedback control,” Applied Mathematics and Computation, vol. 148, no. 1, pp. 35–46, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Weng, “Existence and global stability of positive periodic solution of periodic integrodifferential systems with feedback controls,” Computers & Mathematics with Applications, vol. 40, no. 6-7, pp. 747–759, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  11. F. Yin and Y. Li, “Positive periodic solutions of a single species model with feed-back regulation and distributed time delay,” Applied Mathematics and Computation, vol. 153, pp. 475–484, 2004. View at Publisher · View at Google Scholar
  12. K. Wang, Z. Teng, and H. Jiang, “On the permanence for n-species non-autononous Lotka-Volterra competitive system with infinite delays and feed-back controls,” International Joural of Biomathematics, vol. 1, pp. 29–43, 2008. View at Publisher · View at Google Scholar
  13. F. Chen, J. Yang, L. Chen, and X. Xie, “On a mutualism model with feedback controls,” Applied Mathematics and Computation, vol. 214, no. 2, pp. 581–587, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Teng and Z. Li, “Permanence and asymptotic behavior of the N-species nonautonomous Lotka-Volterra competitive systems,” Computers & Mathematics with Applications, vol. 39, no. 7-8, pp. 107–116, 2000. View at Publisher · View at Google Scholar · View at MathSciNet