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A unified approach to persistence

  • I. Stability and Persistence for Ecological Models
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References

  1. N. P. Bhatia and G. P. Szegö:Stability Theory of Dynamical Systems. Grundlehren math. Wissensch. 161. Berlin-Heidelberg-New York: Springer. 1970.

    Google Scholar 

  2. R. Bowen: ω-limit sets for Axiom A diffeomorphisms, J. Diff. Equ.18, 333–339 (1975).

    Google Scholar 

  3. G. Butler, H. I. Freedman and P. Waltman: Uniformly persistent systems. Proc. Amer. Math. Soc.96, 425–430 (1986).

    Google Scholar 

  4. G. Butler, P. Waltman: Persistence in dynamical systems. J. Diff. Equ.63, 255–263 (1986).

    Google Scholar 

  5. C. Conley:Isolated invariant sets and the Morse index. CBMS 38. Providence, R.I.: Amer. Math. Soc. 1978.

    Google Scholar 

  6. A. Fonda: Uniformly persistent semi-dynamical systems. Proc. Amer. Math. Soc. To appear.

  7. H. I. Freedman and J. W.-H. So: Persistence in discrete semi-dynamical systems. Preprint (1987).

  8. H. I. Freedman and P. Waltman: Mathematical analysis of some three-species food-chain models. Math. Biosci.33, 257–276 (1977).

    Google Scholar 

  9. T. C. Gard and T. G. Hallam: Persistence of food webs: I. Lotka-Volterra food chains. Bull. Math. Biol.41, 877–891 (1979).

    Google Scholar 

  10. B. M. Garay: Uniform persistence and chain recurrence. J. Math. Anal. Appl. To appear.

  11. J. Hofbauer: A general cooperation theorem for hypercycles. Monatsh. Math.91: 233–240 (1981).

    Google Scholar 

  12. J. Hofbauer: Heteroclinic cycles on the simplex. Proc. Int. Conf. Nonlinear Oscillations. Budapest 1987.

  13. J. Hofbauer and K. Sigmund: Permanence for replicator equations. In:Dynamical Systems. Ed. A. B. Kurzhansky and K. Sigmund. Springer Lect. Notes Econ. Math. Systems287. 1987.

  14. J. Hofbauer and K. Sigmund:Dynamical Systems and the Theory of Evolution. Cambridge Univ. Press 1988.

  15. V. Hutson: A theorem on average Ljapunov functions. Monatsh. Math.98, 267–275 (1984).

    Google Scholar 

  16. W. Jansen: A permanence theorem for replicator and Lotka-Volterra systems. J. Math. Biol.25, 411–422 (1987).

    Google Scholar 

  17. G. Kirlinger:Permanence of some four-species Lotka-Volterra systems. Dissertation. Universität Wien. 1987.

  18. C. Robinson: Stability theorems and hyperbolicity in dynamical systems. Rocky Mountain J. Math.7, 425–434 (1977).

    Google Scholar 

  19. P. Schuster, K. Sigmund and R. Wolff: Dynamical systems under constant organization. III. Cooperative and competitive behaviour of hypercycles. J. Diff. Equ.32, 357–368 (1979).

    Google Scholar 

  20. T. Ura and I. Kimura: Sur le courant exterieur a une region invariante. Theoreme de Bendixson. Comm. Math. Univ. Sanctii Pauli8, 23–39 (1960).

    Google Scholar 

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  1. Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090, Wien, Austria

    Josef Hofbauer

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  1. Josef Hofbauer
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Hofbauer, J. A unified approach to persistence. Acta Appl Math 14, 11–22 (1989). https://doi.org/10.1007/BF00046670

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