Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2009 (2009), Article ID 481712, 8 pages
http://dx.doi.org/10.1155/2009/481712
Research Article

Permanence of Periodic Predator-Prey System with General Nonlinear Functional Response and Stage Structure for Both Predator and Prey

School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, Fujian 350007, China

Received 16 September 2009; Revised 24 November 2009; Accepted 6 December 2009

Academic Editor: Stephen Clark

Copyright © 2009 Xuming Huang 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. J. F. Andrews, “A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates,” Biotechnology and Bioengineering, vol. 10, no. 6, pp. 707–723, 1968. View at Publisher · View at Google Scholar
  2. W. Sokol and J. A. Howell, “Kinetics of phenol oxidation by washed cells,” Biotechnology and Bioengineering, vol. 23, no. 9, pp. 2039–2049, 1980. View at Publisher · View at Google Scholar
  3. J. A. Cui and X. Y. Song, “Permanence of predator-prey system with stage structure,” Discrete and Continuous Dynamical Systems. Series B, vol. 4, no. 3, pp. 547–554, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. J. A. Cui and Y. Takeuchi, “A predator-prey system with a stage structure for the prey,” Mathematical and Computer Modelling, vol. 44, no. 11-12, pp. 1126–1132, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. X. 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
  6. 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
  7. C.-Y. Huang, M. Zhao, and L.-C. Zhao, “Permanence of periodic predator-prey system with two predators and stage structure for prey,” Nonlinear Analysis: Real World Applications, vol. 11, no. 1, pp. 503–514, 2009. View at Publisher · View at Google Scholar
  8. R. Xu, M. A. J. Chaplain, and F. A. Davidson, “A Lotka-Volterra type food chain model with stage structure and time delays,” Journal of Mathematical Analysis and Applications, vol. 315, no. 1, pp. 90–105, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Wang, “Research on the suitable living environment of the Rana temporaria chensinensis larva,” Chinese Journal of Zoology, vol. 32, no. 1, pp. 38–41, 1997. View at Google Scholar
  10. X. 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
  11. W. Wang and L. Chen, “A predator-prey system with stage-structure for predator,” Computers & Mathematics with Applications, vol. 33, no. 8, pp. 83–91, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  12. O. Bernard and S. Souissi, “Qualitative behavior of stage-structured populations: application to structural validation,” Journal of Mathematical Biology, vol. 37, no. 4, pp. 291–308, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. W. S. Yang, X. P. Li, and Z. J. Bai, “Permanence of periodic Holling type-IV predator-prey system with stage structure for prey,” Mathematical and Computer Modelling, vol. 48, no. 5-6, pp. 677–684, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. F. D. Chen, “Permanence of periodic Holling type predator-prey system with stage structure for prey,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 1849–1860, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. F. D. Chen and M. S. You, “Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey,” Nonlinear Analysis: Real World Applications, vol. 9, no. 2, pp. 207–221, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. J. A. Cui and X. Y. Song, “Permanence of predator-prey system with stage structure,” Discrete and Continuous Dynamical Systems. Series B, vol. 4, no. 3, pp. 547–554, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. P. Georgescu and G. Morosanu, “Impulsive pertubations of a three-trophic prey-dependent food chain system,” Mathematical and Computer Modelling, vol. 48, no. 7-8, pp. 975–997, 2008. View at Publisher · View at Google Scholar · View at MathSciNet