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Abstract and Applied Analysis
Volume 2013, Article ID 832701, 18 pages
http://dx.doi.org/10.1155/2013/832701
Research Article

Stability and Permanence of a Pest Management Model with Impulsive Releasing and Harvesting

Department of Mathematics, Chongqing Normal University, Chongqing 400047, China

Received 16 January 2013; Accepted 27 February 2013

Academic Editor: Chuangxia Huang

Copyright © 2013 Jiangtao Yang and Zhichun Yang. 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. Georgescu and G. Moroşanu, “Pest regulation by means of impulsive controls,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 790–803, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. T. Zhang, X. Meng, and Y. Song, “The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments,” Nonlinear Dynamics, vol. 64, no. 1-2, pp. 1–12, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  3. Y. Ma, B. Liu, and W. Feng, “Dynamics of a birth-pulse single-species model with restricted toxin input and pulse harvesting,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 142534, 20 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  4. S. Cai, “A stage-structured single species model with pulse input in a polluted environment,” Nonlinear Dynamics, vol. 57, no. 3, pp. 375–382, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. B. Liu, L. Chen, and Y. 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 Zentralblatt MATH · View at MathSciNet
  6. P. Georgescu, H. Zhang, and L. Chen, “Bifurcation of nontrivial periodic solutions for an impulsively controlled pest management model,” Applied Mathematics and Computation, vol. 202, no. 2, pp. 675–687, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. P. Georgescu and H. Zhang, “An impulsively controlled predator-pest model with disease in the pest,” Nonlinear Analysis. Real World Applications, vol. 11, no. 1, pp. 270–287, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. C. Wei and L. Chen, “Eco-epidemiology model with age structure and prey-dependent consumption for pest management,” Applied Mathematical Modelling, vol. 33, no. 12, pp. 4354–4363, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Jiao, S. Cai, and L. Chen, “Analysis of a stage-structured predatory-prey system with birth pulse and impulsive harvesting at different moments,” Nonlinear Analysis. Real World Applications, vol. 12, no. 4, pp. 2232–2244, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  10. J. Jiao, G. Pang, L. Chen, and G. Luo, “A delayed stage-structured predator-prey model with impulsive stocking on prey and continuous harvesting on predator,” Applied Mathematics and Computation, vol. 195, no. 1, pp. 316–325, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Z. Liu and R. Tan, “Impulsive harvesting and stocking in a Monod-Haldane functional response predator-prey system,” Chaos, Solitons and Fractals, vol. 34, no. 2, pp. 454–464, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Nie, Z. Teng, L. Hu, and J. Peng, “The dynamics of a Lotka-Volterra predator-prey model with state dependent impulsive harvest for predator,” Biosystems, vol. 98, no. 2, pp. 67–72, 2009. View at Google Scholar
  13. D. Baĭnov and P. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, John Wiley & Sons, New York, NY, USA, 1993. View at MathSciNet
  14. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989. View at MathSciNet
  15. T. Yang, Impulsive Control Theory, vol. 272, Springer, Berlin, Germany, 2001. View at MathSciNet
  16. C. S. Holling, “The functional response of predators to prey density and its role in mimicry and population regulation,” Memoirs of the Entomological Society of Canada, vol. 45, pp. 5–60, 1965. View at Google Scholar
  17. 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 · View at MathSciNet
  18. C. Shen, “Permanence and global attractivity of the food-chain system with Holling IV type functional response,” Applied Mathematics and Computation, vol. 194, no. 1, pp. 179–185, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. X. Song and Y. Li, “Dynamic behaviors of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect,” Nonlinear Analysis. Real World Applications, vol. 9, no. 1, pp. 64–79, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. B. Liu, Z. Teng, and L. Chen, “Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy,” Journal of Computational and Applied Mathematics, vol. 193, no. 1, pp. 347–362, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. B. Liu, Y. Zhang, and L. Chen, “Dynamic complexities of a Holling I predator-prey model concerning periodic biological and chemical control,” Chaos, Solitons and Fractals, vol. 22, no. 1, pp. 123–134, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. X. Liu and L. Chen, “Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator,” Chaos, Solitons and Fractals, vol. 16, no. 2, pp. 311–320, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. X. Song and Y. Li, “Dynamic complexities of a Holling II two-prey one-predator system with impulsive effect,” Chaos, Solitons & Fractals, vol. 33, no. 2, pp. 463–478, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. S. Zhang, D. Tan, and L. Chen, “Chaos in periodically forced Holling type IV predator-prey system with impulsive perturbations,” Chaos, Solitons and Fractals, vol. 27, no. 4, pp. 980–990, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  25. S. Zhang, F. Wang, and L. Chen, “A food chain model with impulsive perturbations and Holling IV functional response,” Chaos, Solitons and Fractals, vol. 26, no. 3, pp. 855–866, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. L.-L. Wang and W.-T. Li, “Periodic solutions and permanence for a delayed nonautonomous ratio-dependent predator-prey model with Holling type functional response,” Journal of Computational and Applied Mathematics, vol. 162, no. 2, pp. 341–357, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. V. S. Ivlev, Experimental Ecology of the Feeding of Fishes, Yale University Press, New Haven, Conn, USA, 1961.
  28. H. K. Baek, S. D. Kim, and P. Kim, “Permanence and stability of an Ivlev-type predator-prey system with impulsive control strategies,” Mathematical and Computer Modelling, vol. 50, no. 9-10, pp. 1385–1393, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. H. Wang and W. Wang, “The dynamical complexity of a Ivlev-type prey-predator system with impulsive effect,” Chaos, Solitons & Fractals, vol. 38, no. 4, pp. 1168–1176, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. Z. Xiang and X. Song, “The dynamical behaviors of a food chain model with impulsive effect and Ivlev functional response,” Chaos, Solitons & Fractals, vol. 39, no. 5, pp. 2282–2293, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. X. Song, M. Hao, and X. Meng, “A stage-structured predator-prey model with disturbing pulse and time delays,” Applied Mathematical Modelling, vol. 33, no. 1, pp. 211–223, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet