Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2015, Article ID 818506, 11 pages
http://dx.doi.org/10.1155/2015/818506
Research Article

Positive Periodic Solutions of a Neutral Impulsive Predator-Prey Model

School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China

Received 24 September 2014; Revised 23 January 2015; Accepted 24 January 2015

Academic Editor: Bai-Lian Larry Li

Copyright © 2015 Guirong Liu and Xiaojuan Song. 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. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  2. Z. Liu and S. Zhong, “An impulsive periodic predator-prey system with Holling type III functional response and diffusion,” Applied Mathematical Modelling, vol. 36, no. 12, pp. 5976–5990, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. X. Fan, F. Jiang, and H. Zhang, “Dynamics of multi-species competition-predator system with impulsive perturbations and Holling type III functional responses,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 10, pp. 3363–3378, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. M. U. Akhmet, M. Beklioglu, T. Ergenc, and V. I. Tkachenko, “An impulsive ratio-dependent predator-prey system with diffusion,” Nonlinear Analysis: Real World Applications, vol. 7, no. 5, pp. 1255–1267, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. X. Wang, W. Wang, and X. Lin, “Dynamics of a periodic Watt-type predator-prey system with impulsive effect,” Chaos, Solitons & Fractals, vol. 39, no. 3, pp. 1270–1282, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. S. H. Saker and J. O. Alzabut, “Existence of periodic solutions, global attractivity and oscillation of impulsive delay population model,” Nonlinear Analysis: Real World Applications, vol. 8, no. 4, pp. 1029–1039, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. S. Ahmad and I. M. Stamova, “Asymptotic stability of an N-dimensional impulsive competitive system,” Nonlinear Analysis: Real World Applications, vol. 8, no. 2, pp. 654–663, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. J. Hou, Z. Teng, and S. Gao, “Permanence and global stability for nonautonomous N-species Lotka-Valterra competitive system with impulses,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1882–1896, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. R. Shi, X. Jiang, and L. Chen, “A predator-prey model with disease in the prey and two impulses for integrated pest management,” Applied Mathematical Modelling, vol. 33, no. 5, pp. 2248–2256, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. H. Su, B. Dai, Y. Chen, and K. Li, “Dynamic complexities of a predator-prey model with generalized Holling type III functional response and impulsive effects,” Computers & Mathematics with Applications, vol. 56, no. 7, pp. 1715–1725, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. H. Baek, “Species extinction and permanence of an impulsively controlled two-prey one-predator system with seasonal effects,” Biosystems, vol. 98, no. 1, pp. 7–18, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Du and Z. Feng, “Periodic solutions of a neutral impulsive predator-prey model with Beddington-DeAngelis functional response with delays,” Journal of Computational and Applied Mathematics, vol. 258, pp. 87–98, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. G. Liu and J. Yan, “Positive periodic solutions for neutral delay ratio-dependent predator-prey model with Holling type III functional response,” Applied Mathematics and Computation, vol. 218, no. 8, pp. 4341–4348, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. R. E. Gaines and J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Lecture Notes in Mathematics, Vol. 568, Springer, Berlin, Germany, 1977. View at MathSciNet