Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles

David Angeli, Eduardo D. Sontag

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

Strongly monotone systems of ordinary differential equations which have a certain translation-invariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczyński for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a global convergence property.

Original languageEnglish (US)
Pages (from-to)128-140
Number of pages13
JournalNonlinear Analysis: Real World Applications
Volume9
Issue number1
DOIs
StatePublished - Feb 2008

All Science Journal Classification (ASJC) codes

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Chemical reaction networks
  • Enzymatic futile cycles
  • Global stability
  • Monotone systems

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