Journal of Dynamical and Control Systems

, Volume 18, Issue 3, pp 297–307 | Cite as

Analytic integrability of a modified Michaelis-Menten equation



In this work we consider the modified Michaelis-Menten equation in biochemistry \( \dot{x} \) = −a(E − y)x + by; \( \dot{y} \) = a(E − y)x − (b + r)y; \( \dot{z} \) = ry: It models the enzyme kinetics. We contribute to the description of 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 analytically integrable, and in this case we provide an explicit expression for its first integrals.

Key words and phrases

Analytic integrability Michaelis-Menten equation 

2000 Mathematics Subject Classification

34C05 34A34 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Departamento de MatemáticaInstituto Superior TécnicoLisboaPortugal

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