Stable periodic solutions for the hypercycle system

J. Hofbauer, J. Mallet-Paret, Hal Smith

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


We consider the hypercycle system of ODEs, which models the concentration of a set of polynucleotides in a flow reactor. Under general conditions, we prove the omega-limit set of any orbit is either an equilibrium or a periodic orbit. The existence of an orbitally asymptotic stable periodic orbit is shown for a broad class of such systems.

Original languageEnglish (US)
Pages (from-to)423-436
Number of pages14
JournalJournal of Dynamics and Differential Equations
Issue number3
StatePublished - Jul 1991


  • Competitive systems
  • Poincaré-Bendixson
  • cyclic systems
  • hypercycle system
  • monotonicity

ASJC Scopus subject areas

  • Analysis


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