Stable periodic solutions for the hypercycle system

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

Research output: Contribution to journalArticle

30 Citations (Scopus)

Abstract

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
Volume3
Issue number3
DOIs
StatePublished - Jul 1991

Fingerprint

Periodic Orbits
Periodic Solution
Omega Limit Set
Reactor
Orbit
Model
Class

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Stable periodic solutions for the hypercycle system. / Hofbauer, J.; Mallet-Paret, J.; Smith, Hal.

In: Journal of Dynamics and Differential Equations, Vol. 3, No. 3, 07.1991, p. 423-436.

Research output: Contribution to journalArticle

Hofbauer, J. ; Mallet-Paret, J. ; Smith, Hal. / Stable periodic solutions for the hypercycle system. In: Journal of Dynamics and Differential Equations. 1991 ; Vol. 3, No. 3. pp. 423-436.
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