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Analysis of metabolic systems with complex slow and fast dynamics

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Abstract

We briefly review the results of other authors concerning the analysis of systems with time hierarchy, especially the Tikhonov theorem.

A theorem, recently proved by the authors, making possible rigorous analysis of systems with complex fast dynamics is stated and discussed.

A model example of a simple enzymatic reaction with product activation and slow (genetically driven) enzyme turnover is rigorously studied. It is shown that even in such a simple model there exist certain regions of parameters for which fast variables oscillate. Thus the classical Tikhonov theorem is not applicable here and we are forced to use another method-for example the author's presented theorem—or a purely numerical solution. These two methods are compared.

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Authors and Affiliations

  1. Psychiatric Research Institute, Ústavní 91, 181 03, Prague 8-Bohnice, Czechoslovakia

    I. Dvořák

  2. Faculty of Mathematics and Physics, Carolinae University, Sokolovská 83, 18600, Prague 8-Karlín, Czechoslovakia

    J. Šiška

Authors
  1. I. Dvořák
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  2. J. Šiška
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Dvořák, I., Šiška, J. Analysis of metabolic systems with complex slow and fast dynamics. Bltn Mathcal Biology 51, 255–274 (1989). https://doi.org/10.1007/BF02458446

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  • DOI: https://doi.org/10.1007/BF02458446

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