Advanced Search
Article Contents
Article Contents

Hopf periodic orbits for a ratio--dependent predator--prey model with stage structure

Abstract Related Papers Cited by
  • A ratio--dependent predator-prey model with stage structure for prey was investigated in [8]. There the authors mentioned that they were unable to show if such a model admits limit cycles when the unique equilibrium point $E^*$ at the positive octant is unstable.
        Here we characterize the existence of Hopf bifurcations for the systems. In particular we provide a positive answer to the above question showing for such models the existence of small--amplitude Hopf limit cycles being the equilibrium point $E^*$ unstable.
    Mathematics Subject Classification: Primary: 34D23, 92D25.


    \begin{equation} \\ \end{equation}
  • [1]

    W. G. Aiello and H. I. Freedman, A time delay model of single-species growth with stage structure, Math. Biosci., 101 (1990), 139-153.doi: 10.1016/0025-5564(90)90019-U.


    W. G. Aiello, H. I. Freedman and J. Wu, Analysis of a model representing stage-structured population growth with state-dependent time delay, SIAM J. Appl. Math., 52 (1992), 855-869.doi: 10.1137/0152048.


    Y. Kuznetsov, Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, Vol. 112, Springer-Verlag, New York, 2004.doi: 10.1007/978-1-4757-3978-7.


    Z. Li, M. Han and F. Chen, Global stability of a predator-prey system with stage structure and mutual interference, Discrete Contin. Dyn. Syst. Ser. B, 19 (2014), 173-187.doi: 10.3934/dcdsb.2014.19.173.


    K. G. Magnusson, Destabilizing effect of cannibalism on a structured predator-prey system, Math. Biosci., 155 (1999), 61-75.doi: 10.1016/S0025-5564(98)10051-2.


    W. Wang and L. Chen, A predator-prey system with stage structure for predator, Comput. Math. Appl., 33 (1997), 83-91.doi: 10.1016/S0898-1221(97)00056-4.


    R. Xu, Global convergence of a predator-prey model with stage structure and spatio-temporal delay, Discrete Contin. Dyn. Syst. Ser. B, 15 (2011), 273-291.doi: 10.3934/dcdsb.2011.15.273.


    R. Xu, M. A. J. Chaplain and F. A. Davidson, Persistence and global stability of a ratio-dependent predator-prey model with stage structure, Appl. Math. Comput., 158 (2004), 729-744.doi: 10.1016/j.amc.2003.10.012.


    X. Zhang and L. Chen, The stage-structured predator-prey model and optimal harvesting policy, Math. Biosci., 168 (2000), 201-210.doi: 10.1016/S0025-5564(00)00033-X.

  • 加载中

Article Metrics

HTML views() PDF downloads(159) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint