Stability Analysis of a Nonlinear System with Infinite Distributed Delays Describing Cell Dynamics
- Others:
- Biological control of artificial ecosystems (BIOCORE) ; Inria Sophia Antipolis - Méditerranée (CRISAM) ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de la Recherche Agronomique (INRA)-Laboratoire d'océanographie de Villefranche (LOV) ; Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV) ; Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de la Mer de Villefranche (IMEV) ; Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
- Laboratoire des signaux et systèmes (L2S) ; Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
- Dynamical Interconnected Systems in COmplex Environments (DISCO) ; Laboratoire des signaux et systèmes (L2S) ; Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
- Modelling and Analysis for Medical and Biological Applications (MAMBA) ; Inria de Paris ; Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)) ; Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
- Department of Electrical Engineering and Systems at the School of Electrical Engineering ; Tel Aviv University [Tel Aviv]
Description
We want to reconcile some earlier mod-eling ways of the cell cycle in one common framework. Accordingly, we consider a model that contains a compartment where cells may be quiescent for an unlimited time, along with a proliferating phase in which most of the cells may divide, or die, while few of them may be arrested during their cycle for unlimited time. In fact, the cell-cycle arrest may occur for many reasons (DNA damages detected at some checkpoints, insufficient resources for cell grow, drug infusions). We actually extend some early models involving finite distributed delays (taken from [2], [1]) to the case of infinite distributed delays and time-varying parameters. Our main result relies on the construction of a novel Lyapunov-Krasovskii functional, suitable for the analysis of the origin of the system involving infinite distributed delays and time-varying parameters.
Abstract
International audience
Additional details
- URL
- https://hal.inria.fr/hal-01849010
- URN
- urn:oai:HAL:hal-01849010v1
- Origin repository
- UNICA