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Enzyme catalysis in reactors for industrial applications usually require an external intervention of the species involved in the chemical reactions. We analyze the most elementary open enzyme catalysis with competitive inhibition where a time-dependent inflow of substrate and inhibitor supplies is modeled by almost periodic functions. We prove global stability of an almost periodic solution for the non-autonomous dynamical system arising from the mass-law action. This predicts a well behaved situation in which the reactor oscillates with global stability. This is a first case study in the path toward broader global stability results regarding intraspecific and monotone open reaction networks. [ABSTRACT FROM AUTHOR]