Journal of Nonlinear Mathematical Physics

Volume 20, Issue 1, April 2013, Pages 1 - 8

Liouvillian Integrability of a Modified Michaelis-Menten Equation

Authors
Claudia Valls
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais 1049-001, Lisboa, Portugal, cvalls@math.ist.utl.pt
Received 24 May 2012, Accepted 18 September 2012, Available Online 6 January 2021.
DOI
https://doi.org/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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - 1
Pages
1 - 8
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2013.792459How to use a DOI?
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/).

Cite this article

TY  - JOUR
AU  - Claudia Valls
PY  - 2021
DA  - 2021/01
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  - https://doi.org/10.1080/14029251.2013.792459
ID  - Valls2021
ER  -