Qualitative analysis of Beddington-DeAngelis type impulsive predator-prey models

Nonlinear Analysis: Real World Applications

Volumn 11, Issue 3, 2010, Pages 1312-1322

  Baek, H K ^a  

^a Kyungpook National University   (South Korea)

Author keywords

Beddington DeAngelis functional response; Bifurcation theory; Floquet theory; Impulsive differential equation; Predator prey model

Indexed keywords

BEDDINGTON-DE ANGELIS FUNCTIONAL RESPONSE; BIFURCATION THEORY; FLOQUET THEORY; IMPULSIVE DIFFERENTIAL EQUATION; PREDATOR-PREY MODELS;

DIFFERENTIAL EQUATIONS;

BIFURCATION (MATHEMATICS);

EID: 77950917103     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2009.02.021     Document Type: Article

References (18)

1. Beddington J.R. Mutual interference between parasites or predator and its effect on searching efficiency. J. Animal Ecol. 44 (1975) 331-340
2. DeAngelis D.L., Goldstein R.A., and O'Neill R.V. A model for trophic interaction. Ecology 56 (1975) 881-892
3. Skalski G.T., and Gilliam J.F. Functional responses with predator interference: Viable alternatives to the Holling type II mode. Ecology 82 (2001) 3083-3092
4. Fan M., and Kuang Y. Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response. J. Math. Anal. Appl. 295 (2004) 15-39
5. Hwang T.-W. Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response. J. Math. Anal. Appl. 290 (2004) 113-122
6. Cushing J.M. Periodic time-dependent predator-prey systems. SIAM J. Appl. Math. 32 (1977) 82-95
7. Bainov D.D., and Simeonov P.S. Impulsive Differential Equations: Periodic Solutions and Application. Pitman Monographs and Surveys in Pure and Applied Mathematics vol. 66 (1993), Longman Science & Technical, Harlo, UK
8. Lakshmikantham V., Bainov D., and Simeonov P. Theory of Impulsive Differential Equations (1989), World Scientific Publisher, Singapore
9. Liu B., Zhang Y., and Chen L. Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy. Internat. J. Bifur. Chaos 15 2 (2005) 517-531
10. Liu B., Zhang Y., and Chen L. The dynamical behaviors of a Lotka-Volterra predator-prey model concerning integrated pest management. Nonlinearity Anal. 6 (2005) 227-243
11. Makinde O.D. Solving ratio-dependent predator-prey system with constant effort harvesting using Adomian decomposition method. Appl. Math. Comput. 186 (2007) 17-22
12. Xiao D., and Jennings L.S. Bifurcations of a ratio-dependent predator-prey system with constant rate harvesting. SIAM J. Appl. Math. 65 3 (2005) 737-753
13. Zhang S., and Chen L. A study of predator-prey models with the Beddington-DeAngelis functional response and impulsive effect. Chaos Solitons Fractals 27 (2006) 237-248
14. Wang H., and Wang W. The dynamical complexity of a Ivlev-type prey-predator system with impulsive effect. Chaos Solitons Fractals (2007) 10.1016/j.chaos.2007.02.008
15. Wang H., and Wang W. The dynamical complexity of a Ivlev-type prey-predator system with impulsive effect. Chaos Solitons Fractals (2007) 10.1016/j.chaos.2007.02.008
16. Wang W., Wang H., and Li Z. The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy. Chaos Solitons Fractals 32 (2007) 1772-1785
17. Gakkhar S., and Negi K. Pulse vaccination in SIRS epidemic model with non-monotonic incidence rate. Chaos Solitons Fractals 35 (2008) 626-638 2007
18. Lakmeche A., and Arino O. Bifurcation of non trivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dyn. Contin. Discrete Impuls. Syst. 7 (2000) 265-287