Chaotic behavior of a three-species Beddington-type system with impulsive perturbations

Chaos, Solitons and Fractals

Volumn 37, Issue 2, 2008, Pages 438-443

  Wang, Weiming ^a,b   Wang, Hailing ^c   Li, Zhenqing ^a  

^a INSTITUTE OF BOTANY   (China)

^b WENZHOU UNIVERSITY   (China)

^c CHONGQING UNIVERSITY OF POSTS AND TELECOMMUNICATIONS   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; ECOSYSTEMS; PERTURBATION TECHNIQUES;

FOOD CHAIN; FUNCTIONAL RESPONSE; IMPULSIVE PERTURBATIONS; PREDATORS;

BEHAVIORAL RESEARCH;

EID: 40749161156     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2006.09.013     Document Type: Article

References (19)

1. Hirsch M.W., Smale S., and Devaney R.L. Differential equations, dynamical systems, and an introduction to chaos (2004), Academic press of Elsevier, California, America
2. May R.M. Necessity and chance: deterministic chaos in ecology and evolution. Am Math Soc 32 (1995) 291-308
3. Tang S., and Chen L. Chaos in functional response host-parasitoid ecosystem models. Chaos, Solitons & Fractals 13 (2002) 875-884
4. Zhang S., and Chen L. Chaos in three species food chain system with impulsive perturbations. Chaos, Solitons & Fractals 24 (2005) 73-83
5. 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
6. Liu B., Zhang Y., and Chen L. Dynamic complexities of a Holling I predator-prey model concerning periodic biological and chemical control. Chaos, Solitons & Fractals 22 (2004) 123-134
7. Zhang Y., Xiu Z., and Chen L. Dynamic complexity of a two-prey one-predator system with impulsive effect. Chaos, Solitons & Fractals 26 (2005) 131-139
8. Cantrell R.S., and Cosner C. On the dynamics of predator prey models with the Beddington DeAngelis functional response. J Math Anal Appl 257 (2001) 206-222
9. Xiang Z., and Song X. Extinction and permanence of a two-prey two-predator system with impulsive on the predator. Chaos, Solitons & Fractals 29 (2006) 1121-1136
10. Lonngren K.E., Bai E., and Usar A. Dynamics and synchronization of the Hastings-Powell model of the food chain. Chaos, Solitons & Fractals 20 (2004) 387-393
11. Wang F., Zhang S., and Chen L. Permanence and complexity of a three species food chain with impulsive effect on predator. Int J Nonlinear Sci Numer Simulat 6 (2005) 169-180
12. Ma S., and Lu Q. Dynamical bifurcation for a predator-prey metapopulation model with delay. Int J Nonlinear Sci Num Simulat 6 (2005) 13-17
13. Beddington J.R. Mutual interference between parasites or predators and its effect on searching efficiency. J Animal Ecol 44 (1975) 331-340
14. Dimitrov T.D., and Kojouharov V.H. Complete mathematical analysis of predator-prey models with linear prey growth and Beddington-DeAngelis functional response. J Appl Math Comput 162 (2005) 523-538
15. Bainov D.D., and Simeonov P.S. Impulsive differential equations: asymptotic properties of the solutions (1993), World Scientific, Singapore
16. Wang W., and Lian X. A new algorithm for symbolic integral with application. Appl Math Comput 162 (2005) 949-968
17. Li Z., and Wang W. Mechanization for solving SPP by reducing order method. Appl Math Comput 169 (2005) 1028-1037
18. Li Z., Wang W., and Wang H. The dynamics of a Beddington-type system with impulsive control strategy. Chaos, Solitons & Fractals 29 (2006) 1229-1239
19. Li Z., Wang H., and Wang W. The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy. Chaos, Solitons & Fractals 32 5 (2007) 1772-1785