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.
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Leenheer, P.D., Angeli, D. & Sontag, E.D. Monotone Chemical Reaction Networks. J Math Chem 41, 295–314 (2007). https://doi.org/10.1007/s10910-006-9075-z
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DOI: https://doi.org/10.1007/s10910-006-9075-z