Dynamic complexities of a food chain model with impulsive perturbations and Beddington-DeAngelis functional response

Chaos, Solitons and Fractals

Volumn 27, Issue 3, 2006, Pages 768-777

  Zhang, Shuwen ^a   Tan, Dejun ^a   Chen, Lansun ^b  

^a ANSHAN NORMAL UNIVERSITY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTATIONAL COMPLEXITY; FUNCTIONS; MATHEMATICAL MODELS; OSCILLATIONS;

FOOD CHAIN; IMPULSIVE EQUATION; IMPULSIVE PERTURBATIONS; PERTURBATION SKILLS;

PERTURBATION TECHNIQUES;

EID: 23144449908     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.04.047     Document Type: Article

References (19)

1. J.R. Beddington Mutual interference between parasites and its effect on searching efficiency J Animal Ecol 44 1975 331 340
2. D.L. DeAngelis, R.A. Goldstein, and R.V. O'Neill A model for trophic interaction Ecology 56 1975 801 892
3. G. Ruxton, W.S.C. Gurney, and A. DeRoos Interference and generation cycle Theor Popul Biol 42 1992 235 253
4. C. Cosner, D.L. DeAngelis, J.S. Ault, and D.B. Olson Effects of spatial grouping on the functional response of predators Theor Popul Biol 56 1999 65 75
5. A. Klebanoff, and A. Hastings Chaos in three species food chains J Math Biol 32 1994 427 451
6. L. Xianning, and C. Lansun Complex dynamics of Holling type II Lokta-Voltrra predator-prey system with impulsive perturbations on the predator Chaos, Solitons & Fractals 16 2003 311 320
7. Z. Shuwen, D. lingzhen, and C. Lansun The study of predator-prey with defensive ability of prey and impulsive perturbations on the predator Chaos, Solitons & Fractals 23 2005 631 643
8. Z. Shuwen, and C. Lansun Chaos in three species food chain system with impulsive perturbations Chaos, Solitons & Fractals 24 2005 73 83
9. E. Funasaki, and M. Kot Invasion and chaos in a periodically pulsed mass-action chemostat Theor Popul Biol 44 1993 203 224
10. A. Venkatesan, S. Parthasarathy, and M. Lakshmanan Occurrence of multiple period-doubling bifurcation route to chaos in periodically pulsed chaotic dynamical systems Chaos, Solitons & Fractals 18 2003 891 898
11. D. Bainov, and P. Simeonor Impulsive differential equations: Periodic solutions and applications Pitman Monogr Surreysin Pur Appl Math 66 1993
12. B. Shulgin, L. Stone, and I. Agur Pulse vaccination strategy in the SIR epidemic model Bull Math Biol 60 1998 1 26
13. G. Ballinger, and X. Liu Permanence of population growth models with impulsive effects Math Comput Model 26 1997 59 72
14. A. Lakmeche, and O. Arino Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment Dyn Contin Discret Impul Syst 7 2000 265 287
15. J.C. Panetta A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competition, environment Bull Math Biol 58 1996 425 447
16. M.G. Roberts, and R.R. Kao The dynamics of an infectious disease in a population with birth pulses Math Biosci 149 1998 23 36
17. T. Sanyi, and C. Lansun Density-dependent birth rate, birth pulse and their population dynamic consequences J Math Biol 44 2002 185 199
18. V. Laksmikantham, D.D. Bainov, and P.S. Simeonov Theory of impulsive differential equations 1989 World Scientific Singapore
19. T. Sanyi, and C. Lansun Multiple attractors in stage-structured population models with birth pulses Bull Math Biol 65 2003 479 495