Journal of Mathematical Biology

, Volume 30, Issue 7, pp 755–763 | Cite as

Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations

  • Horst R. Thieme
Research Announcement


Conditions are presented under which the solutions of asymptotically autonomous differential equations have the same asymptotic behavior as the solutions of the associated limit equations. An example displays that this does not hold in general.

Key words

Dynamical systems Asymptotic behavior Butler-McGehee lemma Chemostat Epidemics 


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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Horst R. Thieme
    • 1
  1. 1.Department of MathematicsArizona State UniversityTempeUSA

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