<p>In this work, we investigate the dynamical system of irreversible Michaelis–Menten kinetics in enzyme kinetics. We first summarize some important theoretical results such as non-negativity, boundedness or conservation laws for solutions of the time-continuous dynamical system. As our main contribution regarding this time-continuous setting, we demonstrate that the unique equilibrium state is globally exponentially asymptotically stable by providing a suitable Lyapunov-function. Based on the implicit Eulerian time-stepping method, we propose an explicit reformulation of this time-discretization for the numerical simulation. Our main result for the time-discrete dynamical system is that the unique equilibrium state of the time-discretization is globally exponentially asymptotically stable as well. Conclusively, we illustrate our theoretical findings by numerical experiments.</p>