Free access
Issue
ESAIM: M2AN
Volume 35, Number 4, July-August 2001
Page(s) 675 - 690
DOI http://dx.doi.org/10.1051/m2an:2001102
Published online 15 April 2002
  1. J.S. Allen, M.P. Moulton and F.L. Rose, Persistence in an age-structure population for a patch-type environment. Nat. Resour. Model. 4 (1990) 197-214.
  2. J.R. Beddington, C.A. Free and J.H. Lawton, Dynamical complexity in predator-prey models framed in difference equations. Nature 255 (1975) 58-60. [CrossRef]
  3. J.F. Chen, Influence of high dimension terms for qualitative structure of solutions of a second order linear difference system with ordinary coefficient in the neighborhood of a singular point. Acta Math. Appl. Sinica (China) 11 (1988) 299-311.
  4. M.E. Clark and L.J. Gross, Periodic solutions to nonautonomous difference equations. Math. Biosci. 102 (1990) 105-119. [CrossRef] [MathSciNet] [PubMed]
  5. J.M. Cushing, An introduction to structured population dynamics. SIAM Soc. Indus. Appl. Math., Philadelphia (1998).
  6. H.I. Freedman and J.W.-H. So, Persistence in discrete models of a population which may be subjected to harvesting. Nat. Resour. Model. 2 (1987) 135-145.
  7. H.I. Freedman and Y. Takeuchi, Global stability and predator dynamics in a model of prey dispersal in a patchy environment. Nonlinear Anal. TMA 13 (1989) 993-1002. [CrossRef]
  8. H.I. Freedmen and W.H. Josephso, Persistence in discrete semidynamical systems. SIAM J. Math. Anal. 20 (1989) 930-938. [CrossRef] [MathSciNet]
  9. I. Gumowski and C.Mira, Recurrences and discrete dynamics systems. Lect. Notes Math. 809 (1980) 61-96. [CrossRef]
  10. A. Hastings, Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations. Ecology 74 (1993) 1362-1372. [CrossRef]
  11. V. Hutson and K. Schmitt, Permanence and the dynamics of biological systems. Math. Biosci. 111 (1992) 1-71. [CrossRef] [MathSciNet] [PubMed]
  12. U. Krause and P. Ranet, A limit set trichotomy for monotone nonlinear dynamical systems. Nonlinear Anal. TMA 19 (1992) 375-392. [CrossRef]
  13. Y. Kuang and Y. Takeuchi, Predator-prey dynamics in models of prey dispersal in two patch environments. Math. Biosci. 120 (1994) 77-98. [CrossRef] [MathSciNet] [PubMed]
  14. N.R. Leblond, Porcupine caribou herd. Canadian Arctic Resources Comn., Offuwa (1979).
  15. S.A. Levin, Dispersion and population interactions. Amer. Natur. 108 (1974) 207-228. [CrossRef]
  16. J. Li, Persistence in discrete age-structure population models. Bull. Math. Biol. 50 (1992) 351-366.
  17. A. Okubo, Diffusion and ecological problems, math. models. Springer, Berlin (1980).
  18. K. Schumacher, Regions and oscillations in second order predator-prey recurrences. J. Math. Biol. 16 (1983) 221-231.
  19. J.F. Selgrade and G. Namkoong, Stable periodic behavior in a pioneer-climax model. Nat. Resour. Model. 4 (1990) 215-227.
  20. J.G. Skellam, Random dispersal in theoretical populations. Biometrika 38 (1951) 196-218. [CrossRef] [MathSciNet] [PubMed]
  21. H.L. Smith, Cooperative systems of differential equations with concave nonlinearities. Nonlinear Anal. TMA 10 (1986) 1037-1052. [CrossRef]
  22. Y. Takeuchi, Cooperative systems theory and global stability of diffusion models. Acta Appl. Math. 14 (1989) 49-57. [CrossRef] [MathSciNet]
  23. W.D. Wang and L.S. Chen, A predator-prey system with stage-structure for predator. Comput. Math. Appl. 33 (1997) 83-91. [NASA ADS] [CrossRef] [EDP Sciences] [MathSciNet] [PubMed]
  24. A.-A. Yakubu, Prey dominance in discrete predator-prey system with a prey refuge. Math. Biosci. 144 (1997) 155-178. [CrossRef] [MathSciNet] [PubMed]

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