Oscillations and multiple steady states in a cyclic gene model with repression

Hal Smith

Research output: Contribution to journalArticlepeer-review

74 Scopus citations


In this paper we study the cyclic gene model with repression considered by H. T. Banks and J. M. Mahaffy. Roughly, the model describes a biochemical feedback loop consisting of an integer number G of single gene reaction sequences in series. The model leads to a system of functional differential equations. We show that there is a qualitative difference in the dynamics between even and odd G if the feedback repression is sufficiently large. For even G, multiple stable steady states can coexist while for odd G, periodic orbits exist.

Original languageEnglish (US)
Pages (from-to)169-190
Number of pages22
JournalJournal Of Mathematical Biology
Issue number2
StatePublished - Jun 1 1987
Externally publishedYes


  • Biochemical feedback
  • Cyclic gene model
  • Functional differential equations
  • Repression

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


Dive into the research topics of 'Oscillations and multiple steady states in a cyclic gene model with repression'. Together they form a unique fingerprint.

Cite this