Mathematical study of the global dynamics of a concave gene expression model

Ismail Belgacem 1 Jean-Luc Gouzé 1
1 BIOCORE - Biological control of artificial ecosystems
INRA - Institut National de la Recherche Agronomique, CRISAM - Inria Sophia Antipolis - Méditerranée , LOV - Laboratoire d'océanographie de Villefranche
Abstract : We describe in this paper the global dynamical behavior of a mathematical model of expression of polymerase in bacteria. This model is given by a differential system and algebraic equations. We use some tools from monotone systems theory with concavity of nonlinearities to obtain a global qualitative result: either the trivial equilibrium is globally stable, either there exists a unique positive equilibrium which is globally stable in the positive orthant. The same result holds for a class of qualitatively defined functions. Some generalizations of this result are given.
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https://hal.inria.fr/hal-01091655
Contributor : Jean-Luc Gouzé <>
Submitted on : Friday, December 5, 2014 - 5:23:05 PM
Last modification on : Friday, April 5, 2019 - 8:17:00 PM

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Ismail Belgacem, Jean-Luc Gouzé. Mathematical study of the global dynamics of a concave gene expression model. 22nd Mediterranean Conference of Control and Automation (MED), Jun 2014, Palermo, Italy. ⟨10.1109/MED.2014.6961562 ⟩. ⟨hal-01091655⟩

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