HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Conference papers

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.
Complete list of metadata

https://hal.inria.fr/hal-01091655
Contributor : Jean-Luc Gouzé Connect in order to contact the contributor
Submitted on : Friday, December 5, 2014 - 5:23:05 PM
Last modification on : Thursday, January 20, 2022 - 5:28:31 PM

Identifiers

Citation

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⟩

Share

Metrics

Record views

102