Advanced SearchSearch Tips
Dynamical Behaviors of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 56, Issue 1,  2016, pp.47-55
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2016.56.1.47
 Title & Authors
Dynamical Behaviors of a Discrete Predator-Prey System with Beddington-DeAngelis Functional Response
Choi, Yoon-Ho; Baek, Hunki;
  PDF(new window)
In this paper, we consider a discrete predator-prey system obtained from a continuous Beddington-DeAngelis type predator-prey system by using the method in [9]. In order to investigate dynamical behaviors of this discrete system, we find out all equilibrium points of the system and study their stability by using eigenvalues of a Jacobian matrix for each equilibrium points. In addition, we illustrate some numerical examples in order to substantiate theoretical results.
a discrete system;Beddington-DeAngelis functional response;sink;source;
 Cited by
H. N. Agiza, E. M. Elabbasy, H. EL-Metwally and A. A. Elsadany, Chaotic dynamics of a discrete prey-predator model with Holling type II, Nonlinear Analysis:RWA, 10(2009), 116-129. crossref(new window)

R. Arditi and L. R. Ginzburg, Coupling in predator-prey dynamics:ratio-dependence, J. Theor. Biol., 139(1989), 311-326. crossref(new window)

J. R. Beddington, Mutual interference between parasites or predator and its effect on searching effciency, J. Animal Ecol., 44(1975), 331-340. crossref(new window)

J. Chen and S. Yu, Permance for a discrete ratio-dependent predator-prey system with Holling type III functional response and feedback controls, Discrete Dynamics in Nature and Society, Volume 2013, Article ID 326848, 6pages.

G. Chen, Z. Teng and Z. Hu, Analysis of stability for a discrete ratio-dependent predator-prey system, Indian J. Pure Appl. Math., 42(1)(2011), 1-26. crossref(new window)

C. Cosner, D. L. Deangelis, J. S. Ault, and D. B. Olson, Effects of spatial grouing on the functional response of predators, Theoretical Population Biology, 56(1)(1999), 65-75. crossref(new window)

M. Danca, S. Codreanu and B. Bako, Detailed analysis of a nonlinear prey-predator model, J. Biol. Phys., 23(1997), 11-20. 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)

M. Fan and Y. Kuang, Dynamics of a nonautonomous predator-preysy stem with the Beddington-DeAngelis functional response, J. of Math. Anal. and Appl., 295(2004), 15-39. crossref(new window)

T.-W. Hwang, Global analysis of the predator-prey system with Beddington-DeAngelis functional response, J. of Math. Anal. and Appl., 281(2003), 395-401. crossref(new window)

B. Liu, Y. Zhang and L. Chen, Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy, Int. J. of Bifur. and Chaos, 15(2)(2005), 517-531. crossref(new window)

X. Liu and D. Xiao, Complex dynamic behaviors of a discrete-time predator-prey system, Chaos, Solitons and Fractals, 32(2007), 80-94. crossref(new window)

X. Liu and Y. Xing, Bifurcation of a ratio-dependent Holling-Tanner system with refuge and constant havesting, Abstract and Applied Analysis, 2013(2013), Article ID 478315, 1-10.

S. Ruan and D. Xiao, Golbal analysis in a predator-prey sytem with non-monotonic functional response, SIAM J. Appl. Math., 61(4)(2001), 1445-1472. crossref(new window)

E. Saez and E. Gonzalez-Olivares, Dynamics of a predator-prey model, SIAM J. Appl. Math., 59(5)(1999), 1867-1878. crossref(new window)

G. T. Skalsk and J. F. Gilliam, Functional responses with predator interference: Viable alternatives to the Holling type II mode, Ecology, 82(2001), 3083-3092. crossref(new window)

W. Wang, Q.-X. Liu and Z. Jin, Spatiotemporal complexity of a ratio-dependent predator-prey system, Physical Review E, 75(2007), 051913(9). crossref(new window)

T. Wu, Dynamic Behaviors of a discrete two species predator-prey system incorpora-tiong harvesting, Discrete Dynamics in Nature and Society, Volume 2012, Article ID 429076, 12pages.

S. Zhang and L. Chen, A study of predator-prey models with the Beddington-DeAngelis functional response and impulsive effect, Chaos, Solitons and Fractals, 27(2006), 237-248. crossref(new window)