Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 721403, 10 pages
http://dx.doi.org/10.1155/2014/721403
Research Article

Dynamics of a Diffusive Predator-Prey Model with General Nonlinear Functional Response

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

Received 7 August 2013; Accepted 13 November 2013; Published 3 February 2014

Academic Editors: M. Bellassoued, J. Fernández, and J.-L. Liu

Copyright © 2014 Wensheng 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. Chen and J. Shi, “Global stability in a diffusive Holling-Tanner predatorprey model,” Applied Mathematics Letters, vol. 25, no. 3, pp. 614–618, 2012. View at Publisher · View at Google Scholar · View at Scopus
  2. W. Ko and K. Ryu, “Qualitative analysis of a predator-prey model with Holling type II functional response incorporating a prey refuge,” Journal of Differential Equations, vol. 231, no. 2, pp. 534–550, 2006. View at Publisher · View at Google Scholar · View at Scopus
  3. C. V. Pao, “On nonlinear reaction-diffusion systems,” Journal of Mathematical Analysis and Applications, vol. 87, no. 1, pp. 165–198, 1982. View at Google Scholar · View at Scopus
  4. E. Sáez and E. González-Olivares, “Dynamics of a predator-prey model,” SIAM Journal on Applied Mathematics, vol. 59, no. 5, pp. 1867–1878, 1999. View at Google Scholar · View at Scopus
  5. J. T. Tanner, “The stability and the intrinsic growth rates of prey and predator populations,” Ecology, vol. 56, pp. 855–867, 1975. View at Google Scholar
  6. Q. X. Ye and Z. Y. Li, Introduction to Reaction-Diffusion Equations, Science Press, Beijing, China, 1990. View at MathSciNet
  7. C. Duque and M. Lizana, “On the dynamics of a predatorprey model with nonconstant death rate and diffusion,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 2198–2210, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. 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
  9. W. Sokol and J. A. Howell, “Kinetics of phenol oxidation by washed cells,” Biotechnology and Bioengineering, vol. 23, pp. 2039–2049, 1980. View at Google Scholar
  10. V. Hutson and K. Schmitt, “Permanence and the dynamics of biological systems,” Mathematical Biosciences, vol. 111, no. 1, pp. 1–17, 1992. View at Publisher · View at Google Scholar · View at Scopus
  11. J. K. Hale and P. Waltman, “Persistence in infinite-dimensional systems,” SIAM Journal on Mathematical Analysis, vol. 20, no. 2, pp. 388–395, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. P. Grindrod, Patterns and Waves. The Theory and Applications of Reaction-Difusion Equations, Clarendon Press, Oxford, UK, 1991. View at MathSciNet
  13. G. B. Folland, Introduction to Partial Differential Equations, Princeton University Press, 1976. View at MathSciNet
  14. Y. Lou and W.-M. Ni, “Diffusion, self-diffusion and cross-diffusion,” Journal of Differential Equations, vol. 131, no. 1, pp. 79–131, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer, New York, NY, USA, 2nd edition, 1994. View at MathSciNet