Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model

Stéphane Gaubert 1, 2 Thomas Lepoutre 3, 4
2 MAXPLUS - Max-plus algebras and mathematics of decision
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, Polytechnique - X, CNRS - Centre National de la Recherche Scientifique : UMR
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGMC - Centre de génétique moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne], UCBL - Université Claude Bernard Lyon 1 : EA
Abstract : We consider a cell population described by an age-structured partial differential equation with time periodic coefficients. We assume that division only occurs after a minimal age (majority) and within certain time intervals. We study the asymptotic behavior of the dominant Floquet eigenvalue, or Perron-Frobenius eigenvalue, representing the growth rate, as a function of the majority age, when the division rate tends to infinity (divisions become instantaneous). We show that the dominant Floquet eigenvalue converges to a staircase function with an infinite number of steps, determined by a discrete dynamical system. As an intermediate result, we give a structural condition which guarantees that the dominant Floquet eigenvalue is a nondecreasing function of the division rate. We also give a counter example showing that the latter monotonicity property does not hold in general.
Type de document :
Article dans une revue
Journal of Mathematical Biology, Springer Verlag (Germany), 2015, 71 (6), 〈10.1007/s00285-015-0874-3〉
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https://hal.inria.fr/hal-00773211
Contributeur : Thomas Lepoutre <>
Soumis le : vendredi 11 janvier 2013 - 22:42:37
Dernière modification le : mardi 16 janvier 2018 - 16:22:10

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Stéphane Gaubert, Thomas Lepoutre. Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model. Journal of Mathematical Biology, Springer Verlag (Germany), 2015, 71 (6), 〈10.1007/s00285-015-0874-3〉. 〈hal-00773211〉

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