Dynamic complexities of a predator-prey model with generalized Holling type III functional response and impulsive effects

Computers and Mathematics with Applications

Volumn 56, Issue 7, 2008, Pages 1715-1725

  Su, Hua ^a   Dai, Binxiang ^a   Chen, Yuming ^b   Li, Kaiwang ^a  

^a CENTRAL SOUTH UNIVERSITY   (China)

^b WILFRID LAURIER UNIVERSITY   (Canada)

Author keywords

Generalized Holling type III functional response; Impulse; Periodic solution; Permanence; Predator prey model; Stability

Indexed keywords

AGRICULTURAL CHEMICALS; COMPUTER SIMULATION; DYNAMIC MODELS; DYNAMIC RESPONSE; INSECT CONTROL; PEST CONTROL; PESTICIDES; SPRAYING;

COMPLEX DYNAMICS; DIFFERENTIAL SYSTEMS; DYNAMIC COMPLEXITIES; ELSEVIER (CO); FIXED TIMES; FUNCTIONAL RESPONSES; GLOBALLY ASYMPTOTICALLY STABLE (GAS); IMPULSIVE EFFECTS; IMPULSIVE PERTURBATIONS; NATURAL ENEMIES; NUMERICAL SIMULATIONS; PERIODIC SOLUTIONS; PREDATOR PREY; PREDATOR-PREY MODELING;

AGRICULTURAL ENGINEERING;

EID: 48049123276     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2008.04.001     Document Type: Article

References (32)

1. van den Bosch R. The Pesticide Conspiracy (1989), University of California Press
2. Stern V.M., Smith R.F., van den Bosch R., and Hagen K.S. The integrated control concept. Hilgardia 29 (1959) 81-101
3. Akhmet M.U., Beklioglu M., Ergenc T., and Tkachenko V.I. An impulsive ratio-dependent predator-prey system with diffusion. Nonlinear Anal. RWA 7 (2006) 1255-1267
4. B. Dai, H. Su, D. Hu, Periodic solution of a delayed ratio-dependent predator-prey model with monotonic functional response and impulse, Nonlinear Anal. (in press)
5. Georgescu P., and Moroşanu G. Pest regulation by means of impulsive controls. Appl. Math. Comput. 190 (2007) 790-803
6. Hui J., and Zhu D. Dynamic complexities for prey-dependent consumption integrated pest management models with impulsive effects. Chaos Solitons Fractals 29 (2006) 233-251
7. Liu B., Liu W., and Teng Z. Analysis of a predator-prey model concerning impulsive perturbations. Dyn. Contin. Discrete Impuls. Syst. Ser. B Appl. Algorithms 14 (2007) 135-153
8. Liu B., Teng Z., and Chen L. Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy. J. Comput. Appl. Math. 193 (2006) 347-362
9. Liu B., Zhang Y., and Chen L. Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy. Internat. J. Bifurc. Chaos Appl. Sci. Engrg. 15 (2005) 517-531
10. Liu X., and Chen L. Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator. Chaos Solitons Fractals 16 (2003) 311-320
11. J.J. Nieto, D. O'Regan, Variational approach to impulsive differential equations, Nonlinear Anal. RWA (in press)
12. Nieto J.J., and Rodriguez-Lopez R. New comparison results for impulsive integro-differential equations and applications. J. Math. Anal. Appl. 328 (2007) 1343-1368
13. J. Shen, J. Li, Existence and global attractivity of positive periodic solutions for impulsive predato-prey model with dispersion and time delays, Nonlinear Anal. RWA (in press)
14. Tang S., Xiao Y., Chen L., and Cheke R.A. Pest management models and their dynamical behaviour. Bull. Math. Biol. 67 (2005) 115-135
15. W.B. Wang, J.H. Shen, J.J. Nieto, Permanence and periodic solution of predator prey system with Holling type functional response and impulses, Discrete Dyn. Nat. Soc. 2007 (2007), Article ID 81756
16. Zhang H., Chen L., and Nieto J.J. A delayed epidemic model with stage structure and pulses for management strategy. Nonlinear Anal. RWA 9 (2008) 1714-1726
17. Zhang H., Xu W., and Chen L. A impulsive infective transmission SI model for pest control. Math. Methods Appl. Sci. 30 (2007) 1169-1184
18. Zhang S., and Chen L. A study of predator-prey models with the Beddington-DeAnglis functional response and impulsive effect. Chaos Solitons Fractals 27 (2006) 237-248
19. Zhang S., Dong L., and Chen L. The study of predator-prey system with defensive ability of prey and impulsive perturbations on the predator. Chaos Solitons Fractals 23 (2005) 631-643
20. Jiang G., Lu Q., and Qian L. Complex dynamics of a Holling type II prey-predator system with state feedback control. Chaos Solitons Fractals 31 (2007) 448-461
21. Jiang G., Lu Q., and Qian L. Chaos and its control in an impulsive differential system. Chaos Solitons Fractals 34 (2007) 1135-1147
22. Pei Y., Li C., Chen L., and Wang C. Complex dynamics of one-prey multi-predator system with defensive ability of prey and impulsive biological control on predators. Adv. Complex Syst. 8 (2005) 483-495
23. R.K. Upadhyay, V.S.H. Rao, Short-term recurrent chaos and role of Toxin Producing Phytoplankton (TPP) on chaotic dynamics in aquatic systems, Chaos Solitions Fractals (in press)
24. G.Z. Zeng, F.Y. Wang, J.J. Nieto, Complexity of delayed predator-prey model with impulsive harvest and Holling type-II functional response, Adv. Complex Syst. (in press)
25. Zhou J., Xiang L., and Liu Z. Synchronization in complex delayed dynamical networks with impulsive effects. Physica A 384 (2007) 684-692
26. Haddad W.M., Chellaboina V., and Nersesov S.G. Impulsive and Hybrid Dynamical Systems: Stability, Dissipativity, and Control (2006), Princeton University Press, Princeton, NJ
27. Lakshmikantham V., Baǐnov D.D., and Simeonov P.S. Theory of Impulsive Differential Equations (1989), World Scientific Publishing Co., Inc, Teaneck, NJ
28. Zavalishchin S.T., and Sesekin A.N. Dynamic Impulse Systems: Theory and Applications (1997), Kluwer Academic Publishers Group, Dordrecht
29. Zhang H., Chen L., and Georgescu P. Impulsive control strategies for pest management. J. Biol. Syst. 15 (2007) 235-260
30. Sugie J., and Katagama M. Global asymptotic stability of a predator-prey system of Holling type. Nonlinear Anal. 38 (1999) 105-121
31. Sugie J., Kohno R., and Miyazaki R. On a predator-prey system of Holling type. Proc. Amer. Math. Soc. 125 (1997) 2041-2050
32. Baǐnov D., and Simeonov P. Impulsive Differential Equations: Periodic Solutions and Applications (1993), Longman Scientific & Technical, Harlow