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Dynamics of a Discrete Predator-Prey System with Beddington-DeAngelis Function Response

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DOI: 10.4236/am.2012.34060    4,340 Downloads   7,701 Views   Citations

ABSTRACT

This paper discusses the dynamic behaviors of a discrete predator-prey system with Beddington-DeAngelis function response. We first show that under some suitable assumption, the system is permanent. Furthermore, by constructing a suitable Lyapunov function, a sufficient condition which guarantee the global attractivity of positive solutions of the system is established

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Q. Fang, X. Li and M. Cao, "Dynamics of a Discrete Predator-Prey System with Beddington-DeAngelis Function Response," Applied Mathematics, Vol. 3 No. 4, 2012, pp. 389-394. doi: 10.4236/am.2012.34060.

References

[1] J. R. Beddington, “Mutual Interference between Parasites or Predators and Its Effect on Searching Efficiency,” Journal of Animal Ecology, Vol. 44, No. 3, 1975, pp. 331-340. doi:10.2307/3866
[2] D. L. DeAngelis, R. A. Goldstein and R. V. O’Neil, “A Model for Trophic Interaction,” Ecology, Vol. 56, No. 4, 1975, pp. 881-892. doi:10.2307/1936298
[3] H. Y. Li and Y. Takeuchi, “Dynamics of the Density Dependent Predator-Prey System with Beddington-DeAngelis Functional Response,” Journal of Mathematical Analysis and Application, Vol. 374, No. 4, 2011, pp. 644654. doi:10.1016/j.jmaa.2010.08.029
[4] W. J Qin, Z. J. Liu and Y. P. Chen, “Permanence and Global Stability of Positive Periodic Solutions of a Discrete Competitive System,” Discrete Dynamics in Nature and Society, 2009, Article ID 830537.
[5] R. X. Wu and Lin Li, “Permanence and Global Attractivity of Discrete Predator-Prey System with Hassell-Varley Type Functional Response,” Discrete Dynamics in Nature and Society, Applications, Vol. 299, No. 2, 2004, pp. 357-374.
[6] F. Chen, “Permanence and Global Stability of Nonautonomous Lotka-Volterra System with Predator Prey and Deviating Arguments,” Applied Mathematics and Computation, Vol. 173, No. 2, 2006, pp. 1082-1100. doi:10.1016/j.amc.2005.04.035
[7] F. Chen, “Permanence and Global Attractivity of a Discrete Multispecies Lotka-Volterra Competition PredatorPrey Systems,” Applied Mathematics and Computation, Vol. 182, No. 1, 2006, pp. 3-12. doi:10.1016/j.amc.2006.03.026
[8] F. Chen, “Permanence of a Discrete n-Species Food-Chain System with Time Delays,” Applied Mathematics and Computation, Vol. 182, No. 1, 2007, pp. 719-726. doi:10.1016/j.amc.2006.07.079
[9] F. Chen, “Permanence for the Discrete Mutualism Model with Time Delays,” Mathematical and Computer Modelling, Vol. 47, No. 3-4, 2008, pp. 431-435. doi:10.1016/j.mcm.2007.02.023
[10] Y.H. Fan, W.T. Li, “Permanence for a Delayed Discrete Ratio-Dependent Predator-Prey System with Holling Type Functional Response,” Journal of Mathematical Analysis, 009, Article ID 323065.
[11] L. Chen, J. Xu and Z. Li, “Permanence and Global Attractivity of a Delayed Discrete Predator-Prey System with General Holling-Type Functional Response and Feedback Controls,” Discrete Dynamics in Nature and Society, 2008, Article ID 629620.
[12] J. Yang, “Dynamics Behaviors of a discrete ratio-Dependent Predator-Prey System with Holling type III Functional Response and Feedback Controls,” Discrete Dynamics in Nature and Society, Vol. 2008, Article ID 186539.
[13] X. Li and W. Yang, “Permanence of a Discrete PredatorPrey Systems with Beddington-DeAngelis Functional Response and Feedback Controls,” 2008, Article ID 149267.
[14] M. Fan and K. Wang, “Periodic Solutions of a Discrete Time Nonautonomous Ratio-Dependent Predator-Prey System,” Mathematical Computer Modelling, Vol. 35, No. 9-10, 2002, pp. 951-961. doi:10.1016/S0895-7177(02)00062-6

  
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