Global Stability of Full Open Reversible Michaelis-Menten Reactions1

We consider the full closed and open Michaelis-Menten enzymatic reactions. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. Then we consider an open chain of reversible metabolic reactions and also prove global stability. Our mathematical tools are monotone systems theory and compartmental systems theory.