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The Scientific World Journal
Volume 2014, Article ID 824801, 7 pages
http://dx.doi.org/10.1155/2014/824801
Research Article

Feedback Control in a General Almost Periodic Discrete System of Plankton Allelopathy

Department of Mathematics, Hubei Minzu University, Enshi 445000, China

Received 5 August 2013; Accepted 6 November 2013; Published 23 January 2014

Academic Editors: S. Balint and H. Su

Copyright © 2014 Wenshuang Yin. 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. M. Hans, Der Einfluss Einer Pflanze Auf Die Andere: Allelopathie, Verlag von Gustav Fisher, Jena, Germany, 1937.
  2. S. A. Huntsman and R. T. Barber, “Modification of phytoplankton growth by excreted compounds in low density populations,” Journal of Phycology, vol. 11, pp. 10–13, 1975. View at Google Scholar
  3. E. L. Rice, Allelopathy, Academic Press, New York, NY, USA, 2nd edition, 1984.
  4. J. M. Wolfe and E. L. Rice, “Allelopathic interactions among algae,” Journal of Chemical Ecology, vol. 5, no. 4, pp. 533–542, 1979. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. Liu and L. Chen, “Positive periodic solution of a general discrete non-autonomous difference system of plankton allelopathy with delays,” Journal of Computational and Applied Mathematics, vol. 197, no. 2, pp. 446–456, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. Liu, J. Wu, Y. Chen, and M. Haque, “Impulsive perturbations in a periodic delay differential equation model of plankton allelopathy,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 432–445, 2010. View at Publisher · View at Google Scholar · View at Scopus
  7. F. Chen, Z. Li, X. Chen, and J. Laitochová, “Dynamic behaviors of a delay differential equation model of plankton allelopathy,” Journal of Computational and Applied Mathematics, vol. 206, no. 2, pp. 733–754, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. H.-F. Huo and L. I. Wan-Tong, “Permanence and global stability for nonautonomous discrete model of plankton allelopathy,” Applied Mathematics Letters, vol. 17, no. 9, pp. 1007–1013, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. W. Qin and Z. Liu, “Asymptotic behaviors of a delay difference system of plankton allelopathy,” Journal of Mathematical Chemistry, vol. 48, no. 3, pp. 653–675, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. S. N. Zhang, “Existence of almost periodic solutions for difference systems,” Annals of Differential Equations, vol. 16, no. 2, pp. 184–206, 2000. View at Google Scholar
  11. L. Chen, L. Chen, and Z. Li, “Permanence of a delayed discrete mutualism model with feedback controls,” Mathematical and Computer Modelling, vol. 50, no. 7-8, pp. 1083–1089, 2009. View at Publisher · View at Google Scholar · View at Scopus