Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 598539, 14 pages
http://dx.doi.org/10.5402/2012/598539
Research Article

The Study of a Class of Pest Control Pollution Model with Stage-Structure and Time Delay

School of Mathematics and Computer Science, Shaanxi Normal University, Shanxi, Linfen 041004, China

Received 1 March 2012; Accepted 26 March 2012

Academic Editors: A. Bellouquid and C. Lu

Copyright © 2012 Jianwen Jia and Bo Wu. 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. Z. E. Ma, B. J. Song, and T. G. Hallam, “The threshold of survival for systems in a fluctuating environment,” Bulletin of Mathematical Biology, vol. 51, no. 3, pp. 311–323, 1989. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. E. Ma and T. G. Hallam, “Effects of parameter fluctuations on community survival,” Mathematical Biosciences, vol. 86, no. 1, pp. 35–49, 1987. View at Publisher · View at Google Scholar
  3. H. P. Liu and Z. E. Ma, “The threshold of survival for system of two species in a polluted environment,” Journal of Mathematical Biology, vol. 30, no. 1, pp. 49–61, 1991. View at Google Scholar · View at Scopus
  4. B. Liu, Z. Teng, and L. Chen, “The effect of impulsive spraying pesticide on stage-structured population models with birth pulse,” Journal of Biological Systems, vol. 13, no. 1, pp. 31–44, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. Z. Lu, X. Chi, and L. Chen, “Impulsive control strategies in biological control of pesticide,” Theoretical Population Biology, vol. 64, no. 1, pp. 39–47, 2003. View at Publisher · View at Google Scholar · View at Scopus
  6. B. Liu, L. S. Chen, and Y. J. Zhang, “The dynamics of a prey-dependent consumption model concerning impulsive control strategy,” Applied Mathematics and Computation, vol. 169, no. 1, pp. 305–320, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. X. Meng, J. Jiao, and L. Chen, “The dynamics of an age structured predator-prey model with disturbing pulse and time delays,” Nonlinear Analysis, vol. 9, no. 2, pp. 547–561, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. K. Y. Liu, X. Z. Meng, and L. S. Chen, “A new stage structured predator-prey Gomportz model with time delay and impulsive perturbations on the prey,” Applied Mathematics and Computation, vol. 196, no. 2, pp. 705–719, 2008. View at Publisher · View at Google Scholar
  9. G. P. Pang, F. Y. Wang, and L. S. Chen, “Extinction and permanence in delayed stage-structure predator-prey system with impulsive effects,” Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2216–2224, 2009. View at Publisher · View at Google Scholar · View at Scopus
  10. B. Liu, Q. Zhang, and Y. H. Gao, “The dynamics of pest control pollution model with age structure and time delay,” Applied Mathematics and Computation, vol. 216, no. 10, pp. 2814–2823, 2010. View at Publisher · View at Google Scholar
  11. J. Chattopadhyay and O. Arino, “A predator-prey model with disease in the prey,” Nonlinear Analysis B, vol. 36, pp. 747–766, 1999. View at Publisher · View at Google Scholar
  12. E. Venturino, “Epidemics in predator-prey models: diseases in the prey,” in Mathematical Population Dynamics: Analysis of Heterogeneity, O. Arino, D. Axelrod, M. Kimmel, and M. Langlais, Eds., vol. 1 of Theory of Epidemics, pp. 381–393, Wuerz, Winnipeg, Canada, 1995. View at Google Scholar
  13. E. Venturino, “Epidemics in predator-prey models: disease in the predators,” IMA Journal of Mathematics Applied in Medicine and Biology, vol. 19, no. 3, pp. 185–205, 2002. View at Google Scholar · View at Scopus
  14. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  15. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, San Diego, Calif, USA, 1993.
  16. B. Liu, L. S. Chen, and Y. J. Zhang, “The effects of impulsive toxicant input on a population in a polluted environment,” Journal of Biological Systems, vol. 11, no. 3, pp. 265–274, 2003. View at Publisher · View at Google Scholar · View at Scopus