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A Stage-Structured Predator-Prey System with Time Delay and Beddington-DeAngelis Functional Response
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  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 4,  2009, pp.605-618
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.4.605
 Title & Authors
A Stage-Structured Predator-Prey System with Time Delay and Beddington-DeAngelis Functional Response
Wang, Lingshu; Xu, Rui; Feng, Guanghui;
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A stage-structured predator-prey system with time delay and Beddington-DeAngelis functional response is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated. The existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results.
stability;Hopf bifurcation;predator-prey system;stage structure;time delay;Beddington-DeAngelis functional response;
 Cited by
J. R. Beddington, Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol., 44(1975), 331-340. crossref(new window)

F. Berezovskaya, G. Karev, R. Arditi, Parametric analysis of the ratio-dependent predator-prey model, J. Math. Biol., 43(2001), 221-246. crossref(new window)

K. Cooke, Z. Grossman, Discrete delay, distributed delay and stability switches, J. Math. Anal. Appl., 86(1982), 592-627. crossref(new window)

D. L. DeAngelis, R. A. Goldstein, R. V. O'Neill, A model for trophic interaction, Ecology, 56(1975), 881-892. crossref(new window)

B. Hassard, N. Kazarinoff, Y. H. Wan, Theory and Applications of Hopf Bifurcation, London Math Soc. Lect. Notes, Series, 41. Cambridge: Cambridge Univ. Press, 1981.

Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.

Y. Kuang, E. Beretta, Global qualitative analysis of a ratio-dependent predator-prey system, J. Math. Biol., 36(1998), 389-406. crossref(new window)

S. Li, X. Liao and C. Li, Hopf bifurcation in a Volterra prey-predator model with strong kernel, Chaos, Solitons & Fractals, 22(2004), 713-722. crossref(new window)

R. M. May, Stability and Complexity in Model Ecosystem, Princeton Univ. Press, Princeton, 1974.

C. Sun, M. Han and Y. Lin, Analysis of stability and Hopf bifurcation for a delayed logistic equation, Chaos, Solitons & Fractals, 31(2007), 672-682. crossref(new window)

W. Sun, A stage-structure predator-prey system with Beddington-DeAngelis functional response, J. Southwest China Normal University, 30(5)(2005), 800-804.

W.Wang, L. Chen, A predator-prey system with stage-structure for predator, Comput. Math. Appl., 33(1997), 83-91.