About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 580185, 11 pages
http://dx.doi.org/10.1155/2013/580185
Research Article

Global Attractivity of a Periodic Delayed -Species Model of Facultative Mutualism

College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

Received 13 November 2012; Accepted 20 January 2013

Academic Editor: Beatrice Paternoster

Copyright © 2013 Ahmadjan Muhammadhaji and Zhidong Teng. 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. E. P. Odum, Fundamentals of Ecology, Saunders, Philadelphia, Pa, USA, 3rd edition, 1971.
  2. Z. Liu, J. Wu, R. Tan, and Y. Chen, “Modeling and analysis of a periodic delayed two-species model of facultative mutualism,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 893–903, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Chen, J. Shi, and X. Chen, “Periodicity in a Lotka-Volterra facultative mutualism system with several delays,” Chinese Journal of Engineering Mathematics, vol. 21, no. 3, pp. 403–409, 2004. View at MathSciNet
  4. H. Wu, Y. Xia, and M. Lin, “Existence of positive periodic solution of mutualism system with several delays,” Chaos, Solitons & Fractals, vol. 36, no. 2, pp. 487–493, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Hu and Z. Zhang, “Four positive periodic solutions to a Lotka-Volterra cooperative system with harvesting terms,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 1115–1121, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. F. Hui and Z. Wang, “Existence and global attractivity of positive periodic solutions for delay Lotka-Volterra competition patch systems with stocking,” Journal of Mathematical Analysis and Applications, vol. 293, no. 1, pp. 190–209, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z. Liu, R. Tan, Y. Chen, and L. Chen, “On the stable periodic solutions of a delayed two-species model of facultative mutualism,” Applied Mathematics and Computation, vol. 196, no. 1, pp. 105–117, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. G. Lin and Y. Hong, “Periodic solutions to non autonomous predator prey system with delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 3, pp. 1589–1600, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  9. S. Lu, “On the existence of positive periodic solutions to a Lotka Volterra cooperative population model with multiple delays,” Nonlinear Analysis: Theory, Methods & Applications, vol. 68, no. 6, pp. 1746–1753, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Shen and J. Li, “Existence and global attractivity of positive periodic solutions for impulsive predator-prey model with dispersion and time delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 1, pp. 227–243, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. F. Wei and K. Wang, “Global stability and asymptotically periodic solution for nonautonomous cooperative Lotka-Volterra diffusion system,” Applied Mathematics and Computation, vol. 182, no. 1, pp. 161–165, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. 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
  13. F. Yin and Y. Li, “Positive periodic solutions of a single species model with feedback regulation and distributed time delay,” Applied Mathematics and Computation, vol. 153, no. 2, pp. 475–484, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C.-J. Zhao, L. Debnath, and K. Wang, “Positive periodic solutions of a delayed model in population,” Applied Mathematics Letters, vol. 16, no. 4, pp. 561–565, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. L. Zhang, H.-X. Li, and X.-B. Zhang, “Periodic solutions of competition Lotka-Volterra dynamic system on time scales,” Computers & Mathematics with Applications, vol. 57, no. 7, pp. 1204–1211, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Zhang, J. Wu, and Z. Wang, “Periodic solutions of nonautonomous stagestructured cooperative system,” Computers & Mathematics With Applications, vol. 47, no. 4-5, pp. 699–706, 2004. View at Publisher · View at Google Scholar
  17. R. E. Gaines and J. L. Mawhin, Coincidence Degree, and Nonlinear Differential Equations, Springer, Berlin, Germany, 1977. View at MathSciNet