Abstract
This article is a continuation of the work done by N. J. Zabusky and R. H. Hardin [2] on an enzyme-catalyzed unbuffered hydrolysis reaction in a one-dimensional membrane. We consider the “zero-dimensional” approximation to a membrane. The system is then governed by a pair of ordinary differential equations. We give a sufficient condition on the parameters of the system for the existence of a limit cycle and present numerical solutions for realistic parameter ranges. Furthermore, we also give a sketched proof of the existence of a pH front for the stationary solutions of the full system of partial differential equations.
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Dai, LS. On the existence of limit cycles for the enzyme-catalyzed hydrolysis reaction in a zero-dimensional representation of a membrane. J. Math. Biology 10, 375–384 (1980). https://doi.org/10.1007/BF00276096
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DOI: https://doi.org/10.1007/BF00276096