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Original Articles

Dynamics of a discrete-time host–parasitoid system with cannibalism

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Pages 419-435 | Received 09 Feb 2010, Accepted 28 Jul 2010, Published online: 17 Mar 2011

References

  • Allen , L. 2006 . An Introduction to Mathematical Biology , NJ : Prentice-Hall .
  • Bogstad , B. , Lily , G. R. and Mehl , S. 1994 . Cannibalism and year-class strength in Atlantic cod in Arcto-boreal ecosystems . ICES Mar. Sci. Symp. , 198 : 576 – 585 .
  • Cushing , J. M. 1989 . A strong ergodic theorem for some nonlinear matrix models for the dynamics of structured population . Nat. Res. Model. , 3 : 331 – 357 .
  • Cushing , J. M. 1991 . A simple model of cannibalism . Math. Biosci. , 107 : 47 – 54 .
  • Cushing , J. M. CBMS-NSF Regional Conference Series in Applied Mathematics . An Introduction to Structured Population Dynamics , Vol. 71 , SIAM .
  • Cushing , J. M. and Li , J. 1995 . Oscillations caused by cannibalism in a size-structured population model . Canad. Appl. Math. Q , 3 : 155 – 172 .
  • Freedman , H. I. and So , J. 1987 . Persistence in discrete models of a population which may be subjected to harvesting . Nat. Res. Model. , 2 : 135 – 145 .
  • Getto , P. , Dickmann , O. and de Roos , A. 2005 . On the (dis)advantages of cannibalism . J. Math. Biol. , 51 : 695 – 712 .
  • Govaerts , W. and Khoshsiar Ghaziani , R. 2006 . Numerical bifurcation analysis of a nonlinear stage structured cannibalism population model . J. Difference Equ. Appl. , 12 : 1069 – 1085 .
  • Grove , A. and Ladas , G. 2005 . Periodicities in Nonlinear Difference Equations , Boca Raton, FL : CRC Press .
  • Hale , J. 1989 . Asymptotic Behavior of Dissipative Systems , Providence, RI : American Mathematical Society .
  • Hale , J. and Kocak , H. 1991 . Dynamics and Bifurcations , New York : Springer-Verlag .
  • Hofbauer , J. and So , J. 1989 . Uniform persistence and repellors for maps . Proc. Amer. Math. Soc. , 107 : 1137 – 1142 .
  • Jang , S. R.-J. and Baglama , J. 2002 . A nutrient-prey–predator model with intratrophic predation . Appl. Math. Comput. , 129 : 517 – 536 .
  • Jang , S. R.-J. , Baglama , J. and Seshaiyer , P. 2005 . Intratrophic predation in a simple food chain with fluctuating nutrient . Discrete Contin. Dyn. Sys. B , 5 : 335 – 352 .
  • Kohlmeier , C. and Ebenhoh , W. 1995 . The stabilizing role of cannibalism in a predator-prey system . Bull. Math. Biol. , 57 : 401 – 423 .
  • Kon , R. , Saito , Y. and Takeuchi , T. 2004 . Permanence of single-species stage-structured models . J. Math. Biol. , 48 : 515 – 528 .
  • Magnússon , K. 1999 . Destabilizing effect of cannibalism on a structured predator–prey system . Math. Biosci. , 155 : 61 – 75 .
  • Neubert , M. and Kot , M. 1962 . The subcritical collapse of predator populations in discrete time predator prey models . Math. Biosci. , 110 : 45 – 66 .
  • Neubert , M. and Kot , M. 1962 . The subcritical collapse of predator populations in discrete time predator prey models . Math. Biosci. , 110 : 45 – 66 .
  • Neubert , M. and Caswell , H. 2000 . Density-dependent vital rates and their population dynamic consequences . J. Math. Biol. , 41 : 103 – 121 .
  • Sacker , R. 1965 . A new approach to the perturbation theory of invariant surfaces . Comm. Pure Appl. Math. , 18 : 717 – 732 .
  • van der Bosch , F. , de Roos , A. M. and Gabriel , W. 1995 . Cannibalism as a life boat mechanism . J. Math. Biol. , 26 : 619 – 621 .
  • Wiggins , S. 2003 . Introduction to Applied Nonlinear Dynamical Systems and Chaos , 2 , New York : Springer .
  • Wikan , A. 2001 . From chaos to chaos. An analysis of a discrete age structured prey predator model . J. Math. Biol. , 43 : 471 – 500 .
  • Wikan , A. and Eide , A. 2004 . An analysis of a nonlinear stage-structured cannibalism model with application to the northeast arctic cod stock . Bull. Math. Biol. , 66 : 1685 – 1704 .

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