Journal of Mathematical Chemistry

, Volume 41, Issue 3, pp 295–314

Monotone Chemical Reaction Networks

  • Patrick De Leenheer
  • David Angeli
  • Eduardo D. Sontag

DOI: 10.1007/s10910-006-9075-z

Cite this article as:
Leenheer, P.D., Angeli, D. & Sontag, E.D. J Math Chem (2007) 41: 295. doi:10.1007/s10910-006-9075-z

We analyze certain chemical reaction networks and show that every solution converges to some steady state. The reaction kinetics are assumed to be monotone but otherwise arbitrary. When diffusion effects are taken into account, the conclusions remain unchanged. The main tools used in our analysis come from the theory of monotone dynamical systems. We review some of the features of this theory and provide a self-contained proof of a particular attractivity result which is used in proving our main result.


chemical reaction networksmonotone systems

AMS subject classification


Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Patrick De Leenheer
    • 1
  • David Angeli
    • 2
  • Eduardo D. Sontag
    • 3
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA
  2. 2.Dip. di Sistemi e InformaticaUniversitá di FirenzeFirenzeItaly
  3. 3.Department of MathematicsRutgers UniversityNew BrunswickUSA