Copyright © 2013 Shuling Yan 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. A. F. Nindjin, M. A. Aziz-Alaoui, and M. Cadivel, “Analysis of a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay,” Nonlinear Analysis: Real World Applications, vol. 7, no. 5, pp. 1104–1118, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
2. P. H. Leslie, “Some further notes on the use of matrices in population mathematics,” Biometrika, vol. 35, pp. 213–245, 1948. View at Zentralblatt MATH · View at MathSciNet
3. P. H. Leslie, “A stochastic model for studying the properties of certain biological systems by numerical methods,” Biometrika, vol. 45, pp. 16–31, 1958. View at Zentralblatt MATH · View at MathSciNet
4. P. Aguirre, E. González-Olivares, and E. Sáez, “Two limit cycles in a Leslie-Gower predator-prey model with additive Allee effect,” Nonlinear Analysis: Real World Applications, vol. 10, no. 3, pp. 1401–1416, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
5. P. Aguirre, E. González-Olivares, and E. Sáez, “Three limit cycles in a Leslie-Gower predator-prey model with additive Allee effect,” SIAM Journal on Applied Mathematics, vol. 69, no. 5, pp. 1244–1262, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
6. F. Chen, L. Chen, and X. Xie, “On a Leslie-Gower predator-prey model incorporating a prey refuge,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 2905–2908, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
7. X. Guan, W. Wang, and Y. Cai, “Spatiotemporal dynamics of a Leslie-Gower predator-prey model incorporating a prey refuge,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 2385–2395, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
8. T. Faria, “Stability and bifurcation for a delayed predator-prey model and the effect of diffusion,” Journal of Mathematical Analysis and Applications, vol. 254, no. 2, pp. 433–463, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
9. R. Yafia, F. El Adnani, and H. T. Alaoui, “Limit cycle and numerical similations for small and large delays in a predator-prey model with modified Leslie-Gower and Holling-type II schemes,” Nonlinear Analysis: Real World Applications, vol. 9, no. 5, pp. 2055–2067, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
10. B. I. Camara and M. A. Aziz-Alaoui, “Dynamics of a predator-prey model with diffusion,” Dynamics of Continuous, Discrete & Impulsive Systems, vol. 15, no. 6, pp. 897–906, 2008. View at Zentralblatt MATH · View at MathSciNet
11. S. Ruan, “On nonlinear dynamics of predator-prey models with discrete delay,” Mathematical Modelling of Natural Phenomena, vol. 4, no. 2, pp. 140–188, 2009. View at Zentralblatt MATH · View at MathSciNet
12. Y. Song, S. Yuan, and J. Zhang, “Bifurcation analysis in the delayed Leslie-Gower predator-prey system,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 33, no. 11, pp. 4049–4061, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
13. G.-P. Hu and W.-T. Li, “Hopf bifurcation analysis for a delayed predator-prey system with diffusion effects,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 819–826, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
14. W. Zuo and J. Wei, “Stability and Hopf bifurcation in a diffusive predatory-prey system with delay effect,” Nonlinear Analysis: Real World Applications, vol. 12, no. 4, pp. 1998–2011, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
15. F. Dumortier, J. Llibre, and J. C. Artés, Qualitative Theory of Planar Differential Systems, Springer, Berlin, Germany, 2006. View at MathSciNet
16. E. González-Olivares, J. Mena-Lorca, A. Rojas-Palma, and J. D. Flores, “Dynamical complexities in the Leslie-Gower predator-prey model as consequences of the Allee effect on prey,” Applied Mathematical Modelling. Simulation and Computation for Engineering and Environmental Systems, vol. 35, no. 1, pp. 366–381, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
17. J. Wu, Theory and Applications of Partial Functional-Differential Equations, vol. 119, Springer, New York, NY, USA, 1996. View at Publisher · View at Google Scholar · View at MathSciNet
18. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, vol. 191, Academic Press, New York, NY, USA, 1993. View at MathSciNet
19. B. D. Hassard, N. D. Kazarinoff, and Y. H. Wan, Theory and Applications of Hopf Bifurcation, vol. 41, 1981. View at MathSciNet
20. J. K. Hale, Functional Differential Equations, Springer, 1971. View at Zentralblatt MATH · View at MathSciNet