Advertisement

Periodic solutions of a discrete-time nonautonomous predator-prey system with the Beddington-DeAngelis functional response

  • Binxiang Dai
  • Jiezhong Zou
Article

Abstract

In this paper, we investigate a discrete-time non-autonomous predator-prey system with the Beddington-DeAngelis functional response. By using the coincidence degree and the related continuation theorem as well as some priori estimates, easily verifiable sufficient criteria are established for the existence of positive periodic solutions.

AMS Mathematics Subject Classification

39A10 39A12 

Key words and phrases

Predator-prey system coincidence degree Beddington-DeAngelis functional response positive periodic solution 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    F. Jose and V. Santiago,An approximation for prey-predator models with time delay, Physis D110 (1997), 313–322.MATHCrossRefGoogle Scholar
  2. 2.
    Y. N. Xiao and L. S. Chen,Modeling and analysis of predator-prey model with disease in the prey, Math. Biosci.171 (2001), 59–82.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    S. Chen, F. Wang and T. Young,Positive oeriodic solution of two-species ratio-dependent predator-prey system with time delay in two-patch environment, Appl. Math. Comp.150 (2004), 737–748.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    J. R. Beddington,Mutual interference between parasites or predators and its effect on searching efficiency, J. Animal Ecol.44 (1975), 331–340.CrossRefGoogle Scholar
  5. 5.
    C. Cosner, D. L. DeAngelis, J. S. Ault and D. B. Olson,Effects of spatial grouping on the functional response of predators, Theor. Pop. Biol.56 (1999), 65–75.MATHCrossRefGoogle Scholar
  6. 6.
    D. L. DeAngelis, R. A. Goldstein and R. V. O’Neill,A model for trophic interaction, Ecology56 (1975), 881–892.CrossRefGoogle Scholar
  7. 7.
    Tzy-Wei Hwang,Global analysis of the predator-prey system with Beddington-DeAngelis functional response, J. Math. Anal. Appl.281 (2003), 395–401.MATHMathSciNetGoogle Scholar
  8. 8.
    Tzy-Wei Hwang,Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response, J. Math. Anal. Appl.290 (2004), 113–122.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    R. S. Cantrell and C. Cosner,On the dynamics of predator-prey models with the Beddington-DeAngelis functional response, J. Math. Anal. Appl.257 (2001), 206–222.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    R. S. Cantrell and C. Cosner,Effects of domain size on the persistence of populations in a dieeusive food chain model with DeAngelis-Beddington functional response, Natural Resource Modelling14 (2001), 335–367.MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    M. Fan and Y. Kuang,Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response, J. Math. Anal. Appl.295 (2004), 15–39.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    H. I. Freedman,Deterministic Mathematical Models in Population Ecology, Marcel Dekker, New York, 1980.MATHGoogle Scholar
  13. 13.
    R. P. Agarwal,Difference Equations and Inequalities: Theory, Methods and Applications, Monographs and Textbooks in Pure and Applied Mathematics, No. 228, Marcel Dekker, New York, 2000.Google Scholar
  14. 14.
    B. S. Goh,Management and Analysis of Biological Populations, Elsevier Scientific, The Nethelands, 1980.Google Scholar
  15. 15.
    J. D. Murry,Mathematical Biology, Springer-Verlag, New York, 1989.Google Scholar
  16. 16.
    R. E. Gaines and J. L. Mawhin,Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977.MATHGoogle Scholar
  17. 17.
    M. Fan and K. Wang,Periodicity in a delayed ratio-dependent predator-prey system, J. Math. Anal. Appl.262 (2001), 179–190.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    M. Fan and K. Wang,Periodic solutions of a discrete time nonautonomous ratiodependent predator-prey system, Math. and Comp. Modelling35 (2002), 951–961.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Korean Society for Computational & Applied Mathematics and Korean SIGCAM 2007

Authors and Affiliations

  1. 1.School of Mathematical Science and Computing TechnologyCentral South UniversityChangsha, HunanChina

Personalised recommendations