Dynamics behaviors of a discrete ratio-dependent predator-prey system with holling type III functional response and feedback controls

Discrete Dynamics in Nature and Society

Volumn 2008, Issue , 2008, Pages

  Yang, Jinghui ^a  

^a FUZHOU UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 58149496553     PISSN: 10260226     EISSN: 1607887X     Source Type: Journal    
DOI: 10.1155/2008/186539     Document Type: Article

References (29)

1. L.-L. Wang and W.-T. Li, "Existence of periodic solutions of a delayed predator-prey system with functional response," International Journal of Mathematical Sciences, vol. 1, no. 1-2, pp. 55-63, 2002.
2. L.-L. Wang and W.-T. Li, "Existence and global stability of positive periodic solutions of a predatorprey system with delays," Applied Mathematics and Computation, vol. 146, no. 1, pp. 167-185, 2003.
3. W.-T. Li and S.-L. Wu, "Traveling waves in a diffusive predator-prey model with Holling type-III functional response," Chaos, Solitons & Fractals, vol. 37, no. 2, pp. 476-486, 2008.
4. G. Zeng, F. Wang, and J. J. Nieto, "Complexity of a delayed predator-prey model with impulsive harvest and Holling type II functional response," Advances in Complex Systems, vol. 11, no. 1, pp. 77- 97, 2008.
5. M. R. Garvie and C. Trenchea, "Finite element approximation of spatially extended predator-prey interactions with the Holling type II functional response," Numerische Mathematik, vol. 107, no. 4, pp. 641-667, 2007.
6. W. Wang, J. Shen, and J. J. Nieto, "Permanence and periodic solution of predator-prey system with Holling type functional response and impulses," Discrete Dynamics in Nature and Society, vol. 2007, Article ID 81756, 15 pages, 2007.
7. Y. Xia, J. Cao, and M. Lin, "Discrete-time analogues of predator-prey models with monotonic or nonmonotonic functional responses," Nonlinear Analysis: Real World Applications, vol. 8, no. 4, pp. 1079-1095, 2007.
8. H.-F. Huo, W.-T. Li, and J. J. Nieto, "Periodic solutions of delayed predator-prey model with the Beddington-DeAngelis functional response," Chaos, Solitons & Fractals, vol. 33, no. 2, pp. 505-512, 2007.
9. 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.
10. J. J. Nieto and R. Rodríguez-López, "Hybrid metric dynamical systems with impulses," Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 2, pp. 368-380, 2006.
11. T. K. Kar and H. Matsuda, "Global dynamics and controllability of a harvested prey-predator system with Holling type III functional response," Nonlinear Analysis: Hybrid Systems, vol. 1, no. 1, pp. 59-67, 2007.
12. R. Arditi, N. Perrin, and H. Saiah, "Functional response and heterogeneities: An experiment test with cladocerans," Oikos, vol. 60, pp. 69-75, 1991.
13. V. L. Kocic and G. Ladas, Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993.
14. L.-L. Wang and W.-T. Li, "Periodic solutions and permanence for a delayed nonautonomous ratiodependent predator-prey model with Holling type functional response," Journal of Computational and Applied Mathematics, vol. 162, no. 2, pp. 341-357, 2004.
15. C. Chen and K. Ji, "On a non-autonomous ratio-dependent predator-prey system with feedback controls," Journal of Biomathematics, vol. 22, no. 2, pp. 200-208, 2007.
16. B. Dai and J. Zou, "Periodic solutions of a discrete-time diffusive system governed by backward difference equations," Advances in Difference Equations, vol. 2005, no. 3, pp. 263-274, 2005.
17. R. P. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications, vol. 228 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, NY, USA, 2nd edition, 2000.
18. J. D. Murry, Mathematical Biology, Springer, New York, NY, USA, 1989.
19. Y.-H. Fan and W.-T. Li, "Permanence for a delayed discrete ratio-dependent predator-prey system with Holling type functional response," Journal of Mathematical Analysis and Applications, vol. 299, no. 2, pp. 357-374, 2004.
20. H.-F. Huo and W.-T. Li, "Positive periodic solutions of a class of delay differential system with feedback control," Applied Mathematics and Computation, vol. 148, no. 1, pp. 35-46, 2004.
21. F. Chen, "Permanence and global stability of nonautonomous Lotka-Volterra system with predatorprey and deviating arguments," Applied Mathematics and Computation, vol. 173, no. 2, pp. 1082-1100, 2006.
22. F. Chen, "Permanence of a single species discrete model with feedback control and delay," Applied Mathematics Letters, vol. 20, no. 7, pp. 729-733, 2007.
23. F. Chen, "Permanence of a discrete n-species food-chain system with time delays," Applied Mathematics and Computation, vol. 185, no. 1, pp. 719-726, 2007.
24. X. Chen and C. Fengde, "Stable periodic solution of a discrete periodic Lotka-Volterra competition system with a feedback control," Applied Mathematics and Computation, vol. 181, no. 2, pp. 1446-1454, 2006.
25. F. Chen, "On the periodic solutions of periodic multi-species Kolmogorov type competitive system with delays and feedback controls," Applied Mathematics and Computation, vol. 180, no. 1, pp. 366-373, 2006.
26. C. Xiaoxing and C. Fengde, "Almost-periodic solutions of a delay population equation with feedback control," Nonlinear Analysis: Real World Applications, vol. 7, no. 4, pp. 559-571, 2006.
27. F. Chen, "Permanence in nonautonomous multi-species predator-prey system with feedback controls," Applied Mathematics and Computation, vol. 173, no. 2, pp. 694-709, 2006.
28. X. Li and W. Yang, "Permanence of a discrete predator-prey systems with Beddington-DeAngelis functional response and feedback controls," Discrete Dynamics in Nature and Society, vol. 2008, Article ID 149267, 8 pages, 2008.
29. L. Wang and M. Q. Wang, Ordinary Di.erences Equation, Xinjiang University Press, Xinjiang, China, 1991.