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Journal of Mathematical Biology

, Volume 25, Issue 4, pp 411–422 | Cite as

A permanence theorem for replicator and Lotka-Volterra systems

  • Wolfgang Jansen
Article

Abstract

A sufficient criterion for permanence in replicator equations and Volterra equations is derived.

Keywords

Stochastic Process Probability Theory Mathematical Biology Matrix Theory Volterra Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Hofbauer, J.: A general cooperation theorem for hypercycles. Monatsh. Math. 91, 233–240 (1981)Google Scholar
  2. 2.
    Hofbauer, J. Sigmund, K.: Evolutions theorie und dynamische Systeme—Mathematische Aspekte der Evolution. Berlin Hamburg: Paul Parey 1984Google Scholar
  3. 3.
    Schuster, P., Sigmund, K., Hofbauer, J., Wolff, R: Selfregulation of behaviour in animal societies, I-III. Biol. Cybern. 40, 1–25 (1981)Google Scholar
  4. 4.
    Schuster, P., Sigmund, R.: Replicator dynamics. J. Theor. Biol. 100, 533–538 (1983)Google Scholar
  5. 5.
    Schuster, P., Sigmund, K., Wolff, R.: Dynamical systems under constant organisation, I: Bull. Math. Biophys. 40, 743–769 (1978). III: J. Diff. Eq. 32, 357–368 (1979)Google Scholar
  6. 6.
    Zeeman, E. C.: Population dynamics from game theory. In: Global theory of dynamical systems, pp. 471–497. Berlin Heidelberg, New York: Springer 1980Google Scholar
  7. 7.
    Amann, E., Hofbauer, J.: Permanence in Lotka-Volterrá and replicator equations. In: Lotka-Volterra-approach to cooperation and competition in dynamic systems. Berlin: Akademie-Verlag, 1985Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Wolfgang Jansen
    • 1
  1. 1.Zentralinstitut für Kybernetik und InformationsprozesseAkademie der WissenschaftenBerlinGerman Democratic Republic

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