Liouvillian Integrability of a Modified Michaelis-Menten Equation

DOI

10.1080/14029251.2013.792459How to use a DOI?

Keywords

Liouvillian integrability; Michaelis-Menten equation; invariant algebraic surfaces; Darboux first integrals; exponential factors

Abstract

In this work we consider the modified Michaelis-Menten equation in biochemistry

x˙=-a(E-y)x+by,  y˙=a(E-y)x-(b+r)y,  z˙=ry.

It models the enzyme kinetics. We contribute to the understanding of its global dynamics, or more precisely, to the topological structure of its orbits by studying the integrability problem. We prove that a = 0, or r = 0, or E = 0 are the unique values of the parameters for which the system is integrable, and in this case we provide an explicit expression for its first integrals.

Copyright

© 2013 The Authors. Published by Atlantis Press and Taylor & Francis

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Claudia Valls
PY  - 2021
DA  - 2021/01/06
TI  - Liouvillian Integrability of a Modified Michaelis-Menten Equation
JO  - Journal of Nonlinear Mathematical Physics
SP  - 1
EP  - 8
VL  - 20
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2013.792459
DO  - 10.1080/14029251.2013.792459
ID  - Valls2021
ER  -