Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2016, Article ID 2560195, 9 pages
http://dx.doi.org/10.1155/2016/2560195
Research Article

Dynamics of a Seasonally Forced Phytoplankton-Zooplankton Model with Impulsive Biological Control

Department of Mathematics, Sichuan Minzu College, Kangding 626001, China

Received 27 May 2016; Accepted 22 June 2016

Academic Editor: Darko Mitrovic

Copyright © 2016 Jianglin Zhao and Yong Yan. 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. M. Karl, E. A. Law, P. Morris, P. L. B. Williams, and S. Emerson, “Metabolic balance of the open sea,” Nature, vol. 426, no. 11, p. 32, 2003. View at Google Scholar
  2. J. E. Truscott and J. Brindley, “Ocean plankton populations as excitable media,” Bulletin of Mathematical Biology, vol. 56, no. 5, pp. 981–998, 1994. View at Publisher · View at Google Scholar · View at Scopus
  3. C. S. Holling, “The components of predation as revealed by a study of small-mammal predation of the European pine sawfly,” The Canadian Entomologist, vol. 91, no. 5, pp. 293–320, 1959. View at Publisher · View at Google Scholar
  4. J. A. Freund, S. Mieruch, B. Scholze, K. Wiltshire, and U. Feudel, “Bloom dynamics in a seasonally forced phytoplankton-zooplankton model: Trigger mechanisms and timing effects,” Ecological Complexity, vol. 3, no. 2, pp. 129–139, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. T. K. Kar and H. Matsuda, “Global dynamics and controllability of a harvested prey-predator system with Holling type III functional response,” Nonlinear Analysis. Hybrid Systems, vol. 1, no. 1, pp. 59–67, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. I. Siekmann and H. Malchow, “Local collapses in the Truscott-Brindley model,” Mathematical Modelling of Natural Phenomena, vol. 3, no. 4, pp. 114–130, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. P. Olla, “Effect of demographic noise in a phytoplankton-zooplankton model of bloom dynamics,” Physical Review E, vol. 87, no. 1, Article ID 012712, 2013. View at Publisher · View at Google Scholar · View at Scopus
  8. I. Bashkirtseva and L. Ryashko, “Stochastic bifurcations and noise-induced Chaos in a dynamic prey-predator plankton system,” International Journal of Bifurcation and Chaos, vol. 24, no. 9, Article ID 1450109, 7 pages, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. R. K. Upadhyay, “A solution to the evolution-related Truscott-Brindley model for the generalized phytoplankton-zooplankton populations,” http://arxiv.org/abs/1212.5420.
  10. M. Gao, H. Shi, and Z. Li, “Chaos in a seasonally and periodically forced phytoplankton-zooplankton system,” Nonlinear Analysis. Real World Applications, vol. 10, no. 3, pp. 1643–1650, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. Luo, “Phytoplankton-zooplankton dynamics in periodic environments taking into account eutrophication,” Mathematical Biosciences, vol. 245, no. 2, pp. 126–136, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. H. Yu, M. Zhao, Q. Wang, and R. P. Agarwal, “A focus on long-run sustainability of an impulsive switched eutrophication controlling system based upon the Zeya reservoir,” Journal of the Franklin Institute, vol. 351, no. 1, pp. 487–499, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. J. Yang and M. Zhao, “A mathematical model for the dynamics of a fish algae consumption model with impulsive control strategy,” Journal of Applied Mathematics, vol. 2012, Article ID 452789, 17 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. L. Wang, L. Chen, and J. J. Nieto, “The dynamics of an epidemic model for pest control with impulsive effect,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1374–1386, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. H. Baek, Y. Do, and Y. Saito, “Analysis of an impulsive predator-prey system with Monod-Haldane functional response and seasonal effects,” Mathematical Problems in Engineering, vol. 2009, Article ID 543187, 16 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. P. Georgescu and H. Zhang, “An impulsively controlled pest management model with n predator species and a common prey,” Bio Systems, vol. 110, no. 3, pp. 162–170, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. Z. Teng, “Uniform persistence of the periodic predator-prey Lotka-Volterra systems,” Applicable Analysis, vol. 72, no. 3-4, pp. 339–352, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  18. H. Guo and X. Song, “An impulsive predator-prey system with modified Leslie-Gower and Holling type II schemes,” Chaos, Solitons and Fractals, vol. 36, no. 5, pp. 1320–1331, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  19. S. Rinaldi, S. Muratori, and Y. Kuznetsov, “Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities,” Bulletin of Mathematical Biology, vol. 55, no. 1, pp. 15–35, 1993. View at Publisher · View at Google Scholar · View at Scopus