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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 371852, 9 pages
http://dx.doi.org/10.1155/2015/371852
Research Article

Dynamical Behaviors of a Stage-Structured Predator-Prey Model with Harvesting Effort and Impulsive Diffusion

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

Received 25 January 2015; Revised 9 May 2015; Accepted 13 May 2015

Academic Editor: Gian I. Bischi

Copyright © 2015 Lingzhi Huang 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. S. A. Levin, “Dispersion and population interactions,” The American Naturalist, vol. 108, pp. 207–228, 1974. View at Google Scholar
  2. S. A. Levin, “Spatial patterning and the structure of ecological communities,” in Some Mathematical Questions in Biology, American Mathematical Society, Providence, RI, USA, 1976. View at Google Scholar
  3. E. Beretta and Y. Takeuchi, “Global stability of single-species diffusion Volterra models with continuous time delays,” Bulletin of Mathematical Biology, vol. 49, no. 4, pp. 431–448, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. E. Beretta and Y. Takeuchi, “Global asymptotic stability of Lotka-Volterra diffusion models with continuous time delay,” SIAM Journal on Applied Mathematics, vol. 48, no. 3, pp. 627–651, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. J. Hui and L.-S. Chen, “A single species model with impulsive diffusion,” Acta Mathematicae Applicatae Sinica: English Series, vol. 21, no. 1, pp. 43–48, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. W. G. Aiello and H. I. Freedman, “A time-delay model of single-species growth with stage structure,” Mathematical Biosciences, vol. 101, no. 2, pp. 139–153, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. J. J. Jiao, X. S. Yang, S. H. Cai, and L. Chen, “Dynamical analysis of a delayed predator-prey model with impulsive diffusion between two patches,” Mathematics and Computers in Simulation, vol. 80, no. 3, pp. 522–532, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. Y. Shao and Y. Li, “Dynamical analysis of a stage structured predator prey system with impulsive diffusion and generic functional response,” Mathematics and Computers in Simulation, vol. 80, pp. 522–532, 2009. View at Publisher · View at Google Scholar
  9. J. Jiao, “The effect of impulsive diffusion on dynamics of a stage-structured predator-prey system,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 716932, 17 pages, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. Y. Shao, “Analysis of a delayed predator-prey system with impulsive diffusion between two patches,” Mathematical and Computer Modelling, vol. 52, no. 1-2, pp. 120–127, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. J. Dhar and K. S. Jatav, “Mathematical analysis of a delayed stage-structured predator-prey model with impulsive diffusion between two predators territories,” Ecological Complexity, vol. 16, pp. 59–67, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. H. L. Smith, “Cooperative systems of differential equations with concave nonlinearities,” Nonlinear Analysis: Theory, Methods & Applications, vol. 10, no. 10, pp. 1037–1052, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  13. X. Song and L. Chen, “Optimal harvesting and stability for a two-species competitive system with stage structure,” Mathematical Biosciences, vol. 170, no. 2, pp. 173–186, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus