Journal of Mathematical Biology

, Volume 30, Issue 7, pp 755–763

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

  • Horst R. Thieme
Research Announcement

DOI: 10.1007/BF00173267

Cite this article as:
Thieme, H.R. J. Math. Biol. (1992) 30: 755. doi:10.1007/BF00173267


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 

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

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

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