Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 37 No. 2 (2019): Revista Integración, temas de matemáticas
Research and Innovation Articles

Oscillations in enzymatic reactions with periodic input

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  • Brenda Lara-Aguilar,
  • Osvaldo Osuna,
  • Giovanni Wences
Brenda Lara-Aguilar
Universidad Michoacana de San Nicolás de Hidalgo, Instituto de Física y Matemáticas, Michoacán, México
Osvaldo Osuna
Universidad Michoacana de San Nicolás de Hidalgo, Instituto de Física y Matemáticas, Michoacán, México.
Giovanni Wences
Universidad Autónoma de Guerrero, Escuela Superior de Matemáticas Núm. 2, Guerrero, México.
DOI: https://doi.org/10.18273/revint.v37n2-2019005

Published 2019-07-29

Keywords

  • Cooperative systems,
  • enzyme kinetics,
  • periodic orbits

How to Cite

Lara-Aguilar, B., Osuna, O., & Wences, G. (2019). Oscillations in enzymatic reactions with periodic input. Revista Integración, Temas De matemáticas, 37(2), 299–306. https://doi.org/10.18273/revint.v37n2-2019005

Abstract

In this work, we prove the existence of periodic solutions for
some enzyme catalysed reaction models subject to periodic substrate input. We also obtain uniqueness and asymptotic stability of the periodic solution of some classes of reaction equations. Numerical simulations are performed using specific substrate functions to illustrate our analytical findings.

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References

[1] Katriel G., “Existence of periodic solutions for enzyme-catalysed reactions with periodic substrate input”, Discrete Contin. Dyn. Syst., Dynamical systems and differential equations. Proceedings of the 6th AIMS International Conference (2007), 551–557, doi:10.3934/proc.2007.2007.551.

[2] Korman P., “A periodic model for the dynamics of cell volume”, Ann. Polon. Math. 116 (2016), No. 3, 243–249.

[3] Muller S. and Regensburger G., “Generalized mass action systems: Complex balancing equilibria and sign vectors of the stoichiometric and kinetic-order subspaces”, SIAM J. Appl. Math. 72 (2012), No. 6, 1926–1947.

[4] Smith H., Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Mathematical Surveys and Monographs. 41, American Mathematical Society, 1995.

[5] Stoleriu I., Davidson F.A. and Liu J.L., “Effects of periodic input on the quasi-steady state assumptions for enzyme-catalysed reactions”, J. Math. Biol. 50 (2005), No. 2, 115–132.