Asymptotically autonomous differential equations in the plane

Horst Thieme

Research output: Contribution to journalArticlepeer-review

139 Scopus citations


We present a couple of examples where the solutions of asymptotically autonomous differential equations behave quite differently from the solutions of the correspond­ing limit equations. Nevertheless a Poincaré Bendixson type limit set trichotomy can be shown in the plane.

Original languageEnglish (US)
Pages (from-to)351-380
Number of pages30
JournalRocky Mountain Journal of Mathematics
Issue number1
StatePublished - 1993


  • Asymptotically autonomous
  • Butler and McGehee Lemma
  • Chemostat
  • Closed (periodic) orbits
  • Cyclical chains
  • Differential equations
  • Domain of attraction
  • Dulac (divergence) criterion
  • Dynamical sys­tems
  • Epidemics
  • Equilibria
  • Global stability
  • Gradostat
  • Limit equations
  • Limit set trichotomy
  • Poincaré & bendixson theorem
  • Undamped duffing oscillator
  • W-limit sets

ASJC Scopus subject areas

  • General Mathematics


Dive into the research topics of 'Asymptotically autonomous differential equations in the plane'. Together they form a unique fingerprint.

Cite this