Properties of the Michaelis-Menten Mechanism in Phase Space

Details Properties of the Michaelis-Menten Mechanism in Phase Space Properties of the Michaelis-Menten Mechanism in Phase Space

2006-11-05

arxiv.org/abs/math/0611119v2

J. Math. Anal. Appl. 339 (2008) 1044-1064

Mathematics

Dynamical Systems

29 pages, 8 figures, corrected a few typos and incorporated reviewer suggestions

Scientific paper

10.1016/j.jmaa.2007.06.078

We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity.

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