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Mathematical Problems in Engineering
Volume 2013, Article ID 168979, 8 pages
http://dx.doi.org/10.1155/2013/168979
Research Article

Optimal Control of Agricultural Insects with a Stage-Structured Model

1School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116029, China
2Department of Mathematics, Anshan Normal University, Anshan, Liaoning 114007, China

Received 13 May 2013; Accepted 8 July 2013

Academic Editor: Hai-Feng Huo

Copyright © 2013 Baolin Kang et al. 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. R. M. Nisbet, S. P. Blythe, W. S. C. Gurney, and J. A. J. Metz, “Stage-structure models of populations with distinct growth and development processes,” IMA Journal of Mathematics Applied, vol. 2, no. 1, pp. 57–68, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. R. M. Nisbet, W. S. C. Gurney, and J. A. J. Metz, “Stage structure models applied in evolutionary ecology,” Biomathematics, vol. 18, pp. 428–449, 1989. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. A. Gourley and Y. Kuang, “A stage structured predator-prey model and its dependence on maturation delay and death rate,” Journal of Mathematical Biology, vol. 49, no. 2, pp. 188–200, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. Y. Fan and L. Chen, “Periodic solutions and period-similarity of a growth model with age-structured population,” Systems Science and Mathematical Sciences, vol. 4, no. 2, pp. 148–158, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Cui, L. Chen, and W. Wang, “The effect of dispersal on population growth with stage-structure,” Computers & Mathematics with Applications, vol. 39, no. 1-2, pp. 91–102, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. X.-A. Zhang, L. Chen, and A. U. Neumann, “The stage-structured predator-prey model and optimal harvesting policy,” Mathematical Biosciences, vol. 168, no. 2, pp. 201–210, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. Xiao and L. Chen, “Analysis of a SIS epidemic model with stage structure and a delay,” Communications in Nonlinear Science & Numerical Simulation, vol. 6, no. 1, pp. 35–39, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Y. Xiao and L. Chen, “Effects of toxicants on a stage-structured population growth model,” Applied Mathematics and Computation, vol. 123, no. 1, pp. 63–73, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. H. Zhang, L. Chen, and R. Zhu, “Permanence and extinction of a periodic predator-prey delay system with functional response and stage structure for prey,” Applied Mathematics and Computation, vol. 184, no. 2, pp. 931–944, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. B. Liu, Q. Zhang, and Y. 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 · View at Zentralblatt MATH · View at MathSciNet
  11. S. Tang, J. Liang, Y. Xiao, and R. A. Cheke, “Sliding bifurcations of Filippov two stage pest control models with economic thresholds,” SIAM Journal on Applied Mathematics, vol. 72, no. 4, pp. 1061–1080, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Gao and L. Chen, “The effect of seasonal harvesting on a single-species discrete population model with stage structure and birth pulses,” Chaos, Solitons & Fractals, vol. 24, no. 4, pp. 1013–1023, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, vol. 6 of Series in Modern Applied Mathematics, World Scientific, Singapore, 1989. View at MathSciNet
  14. D. D. Baĭnov and P. S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, vol. 66 of Chapman and Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific & Technical, New York, NY, USA, 1993. View at MathSciNet
  15. D. D. Baĭnov and P. S. Simeonov, Systems with Impulse Effect: Stability, Theory and Applications, John Wiley & Sons, New York, NY, USA, 1989.
  16. Z. Jin, M. Haque, and Q. Liu, “Pulse vaccination in the periodic infection rate SIR epidemic model,” International Journal of Biomathematics, vol. 1, no. 4, pp. 409–432, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. S. Sun and L. Chen, “Permanence and complexity of the eco-epidemiological model with impulsive perturbation,” International Journal of Biomathematics, vol. 1, no. 2, pp. 121–132, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. Z. Xiong, Y. Xue, and S. Li, “A food chain system with holling IV functional responses and impulsive effect,” International Journal of Biomathematics, vol. 1, no. 3, pp. 361–375, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. X. Meng and Z. Li, “The dynamics of plant disease models with continuous and impulsive cultural control strategies,” Journal of Theoretical Biology, vol. 266, no. 1, pp. 29–40, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  20. S. Tang, G. Tang, and R. A. Cheke, “Optimum timing for integrated pest management: modelling rates of pesticide application and natural enemy releases,” Journal of Theoretical Biology, vol. 264, no. 2, pp. 623–638, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  21. G. Jiang, Q. Lu, and L. Peng, “Impulsive control of a stage-structured pest management system,” Journal of Mathematical Study, vol. 2, no. 2, pp. 329–344, 2005. View at Google Scholar
  22. S. Tang and R. A. Cheke, “State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences,” Journal of Mathematical Biology, vol. 50, no. 3, pp. 257–292, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. G. Jiang, Q. Lu, and L. Peng, “Impulsive ecological control of a stage-structured pest management system,” Mathematical Biosciences and Engineering, vol. 2, no. 2, pp. 329–344, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet