Matt S. Calder, David Siegel
Published 2006-11-05, updated 2010-03-21Version 2
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.
Comments: 29 pages, 8 figures, corrected a few typos and incorporated reviewer suggestions
Journal: J. Math. Anal. Appl. 339 (2008) 1044-1064
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Minimal Dynamical System for $\mathbb{R}^n$
Asymptotic behaviour of self-contracted planar curves and gradient orbits of convex functions
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