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Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 251942, 19 pages
http://dx.doi.org/10.1155/2012/251942
Research Article

The Mathematical Study of Pest Management Strategy

Minnan Science and Technology Institute, Fujian Normal University, Quanzhou, Fujian 362332, China

Received 3 October 2012; Accepted 14 November 2012

Academic Editor: Leonid Shaikhet

Copyright © 2012 Jinbo Fu and Yanzhen Wang. 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. P. S. Simeonov and D. D. Baĭnov, “Orbital stability of periodic solutions of autonomous systems with impulse effect,” International Journal of Systems Science, vol. 19, no. 12, pp. 2561–2585, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. V. Lakshmikantham, D. Bainov, and P. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  3. D. Baĭnov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66, Longman Scientific & Technical, Harlow, UK, 1993.
  4. I. M. Stamova, “Vector Lyapunov functions for practical stability of nonlinear impulsive functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 325, no. 1, pp. 612–623, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. Y. Zhang and J. Sun, “Stability of impulsive functional differential equations,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 68, no. 12, pp. 3665–3678, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. C. Li, J. Sun, and R. Sun, “Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1186–1198, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. L. Chen and J. Sun, “Nonlinear boundary value problem of first order impulsive functional differential equations,” Journal of Mathematical Analysis and Applications, vol. 318, no. 2, pp. 726–741, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. H. Cheng, F. Wang, and T. Zhang, “Multi-state dependent impulsive control for holling i predator-prey model,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 181752, 2012. View at Publisher · View at Google Scholar
  9. Y. Wang and M. Zhao, “Dynamic analysis of an impulsively controlled predator-prey model with Holling type IV functional response,” Discrete Dynamics in Nature and Society, vol. 2012, Article ID 141272, 18 pages, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. L. Shen, E. Feng, and Q. Wu, “Impulsive control in microorganisms continuous fermentation,” International Journal of Biomathematics, vol. 5, no. 2, 2012. View at Publisher · View at Google Scholar
  11. C. Li and S. Tang, “The effects of timing of pulse spraying and releasing periods on dynamics of generalized predator-prey model,” International Journal of Biomathematics, vol. 5, no. 1, 2012. View at Publisher · View at Google Scholar
  12. B. Liu, Y. Tian, and B. Kang, “Dynamics on a Holling II predator-prey model with state-dependent impulsive control,” International Journal of Biomathematics, vol. 5, no. 3, 2012. View at Publisher · View at Google Scholar
  13. L. Chen, Mathematical Model in the Ecology of Application and Research, Science Press, Beijing, China, 1998.
  14. S. Tang and L. Chen, “Density-dependent birth rate, birth pulses and their population dynamic consequences,” Journal of Mathematical Biology, vol. 44, no. 2, pp. 185–199, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. S. Tang and L. Chen, “Impulsive semi-dynamical systems with applications in biological management(the doctor degree’s article),” Chinese Academy of Sciences, 2003 (Chinese).
  16. G. Zeng, L. Chen, and L. Sun, “Existence of periodic solution of order one of planar impulsive autonomous system,” Journal of Computational and Applied Mathematics, vol. 186, no. 2, pp. 466–481, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. G. Zeng, “State dependent on impulsive differential equation periodic solution existence and its application in pest management,” Journal of Biomathematics, vol. 22, no. 4, pp. 652–660, 2007.