Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2011, Article ID 783136, 14 pages
http://dx.doi.org/10.1155/2011/783136
Research Article

Stability Analysis of Three-Species Almost Periodic Competition Models with Grazing Rates and Diffusions

1Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network control & Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China
3Automation Institute, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
4College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 10 May 2011; Accepted 2 June 2011

Academic Editor: Zhengqiu Zhang

Copyright © 2011 Chang-you Wang et al. 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. P. Jiang, “Some periodic ecological models with grazing rates,” Journal of Biomathematics, vol. 5, no. 1, pp. 80–89, 1990 (Chinese). View at Google Scholar
  2. Q. C. Lin, “Some almost periodic biological models with grazing rates,” Journal of Biomathematics, vol. 14, no. 3, pp. 257–263, 1999 (Chinese). View at Google Scholar · View at Zentralblatt MATH
  3. F. D. Chen and X. X. Chen, “The n-competing Lotka-Volterra almost periodic systems with grazing rates,” Journal of Biomathematics, vol. 18, no. 4, pp. 411–416, 2003 (Chinese). View at Google Scholar
  4. Z. Q. Zhang and Z. C. Wang, “Periodic solution for a two-species nonautonomous competition Lotka-Volterra patch system with time delay,” Journal of Mathematical Analysis and Applications, vol. 265, no. 1, pp. 38–48, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Z. Q. Zhang and Z. C. Wang, “Multiple positive periodic solutions for a generalized delayed population model with an exploited term,” Science in China Series A, vol. 50, no. 1, pp. 27–34, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. D. Hu and Z. Q. Zhang, “Four positive periodic solutions of a discrete time delayed predator-prey system with nonmonotonic functional response and harvesting,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3015–3022, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. C. V. Pao and Y.M. Wang, “Numerical solutions of a three-competition Lotka-Volterra system,” Applied Mathematics and Computation, vol. 204, no. 1, pp. 423–440, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. Y. Q. Liu, S. L. Xie, and Z. D. Xie, “Existence and stability for periodic solution of competition reaction-diffusion models with grazing rates in population dynamics,” Journal of Systems Science and Systems Engineering, vol. 10, no. 2, pp. 402–410, 1996. View at Google Scholar
  9. C. Y. Wang, S. Q. An, and C. J. Fang, “Almost periodic solutions and periodic solutions of reaction-diffusion systems with time delays,” Mathematica Applicata, vol. 20, no. 2, pp. 281–285, 2007 (Chinese). View at Google Scholar · View at Zentralblatt MATH
  10. F. D. Chen and C. L. Shi, “Global attractivity in an almost periodic multi-species nonlinear ecological model,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 376–392, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. C. Y. Wang, “Existence and stability of periodic solutions for parabolic systems with time delays,” Journal of Mathematical Analysis and Applications, vol. 339, no. 2, pp. 1354–1361, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. C. Y. Wang, S. Wang, and L. R. Li, “Periodic solution and almost periodic solution for a nonmonotone reaction-diffusion system with time delay,” Acta Mathematica Scientia Series A, vol. 30, no. 2, pp. 517–524, 2010 (Chinese). View at Google Scholar
  13. X. Q. Liu, “Periodic or almost periodic solutions to a class of systems of reaction-diffusion equations,” Chinese Journal of Engineering Mathematics, vol. 11, no. 4, pp. 107–111, 1994 (Chinese). View at Google Scholar
  14. Y. Li and Y. Kuang, “Periodic solutions of periodic delay Lotka-Volterra equations and systems,” Journal of Mathematical Analysis and Applications, vol. 255, no. 1, pp. 260–280, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. C. Y. Wang and X. H. Hu, “Existence and uniqueness of bounded solution and periodic solution of reaction-diffusion equation with time delay,” Journal of Chongqing University of Posts and Telecommunication (Natural Science Edition), vol. 17, no. 5, pp. 644–646, 2005 (Chinese). View at Google Scholar
  16. C. Y. Wang, “Periodic solution of prey predator model with diffusion and distributed delay effects,” Journal of Chongqing University of Posts and Telecommunication (Natural Science Edition), vol. 18, no. 3, pp. 409–412, 2006. View at Google Scholar
  17. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, NY,USA, 1992.
  18. A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974.