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Stability analysis of PDE’s modelling cell dynamics in Acute Myeloid Leukemia

Jose Luis Avila Alonso 1, 2 Catherine Bonnet 1, 2 Emilia Fridman 3 Frédéric Mazenc 1, 2 Jean Clairambault 4, 5
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
2 L2S - Laboratoire des signaux et systèmes
3 Department of Electrical Engineering
4 LJLL - Laboratoire Jacques-Louis Lions
5 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : In this paper we perform a stability analysis oftwo systems of partial differential equations (PDEs) modellingcell dynamics in Acute Myeloid Leukemia. By using a Lyapunovapproach, for an equilibrium point of interest, we obtain stabilitybounds depending on the parameters of the systems. First,we derive sufficient conditions for boundedness of solutions.Then, asymptotic stability conditions are obtained. The resultsare illustrated with numerical examples and simulations.
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Conference papers
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https://hal.inria.fr/hal-01110304
Contributor : Catherine Bonnet <>
Submitted on : Tuesday, January 27, 2015 - 7:03:00 PM
Last modification on : Thursday, July 9, 2020 - 4:08:02 PM

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CNRS | INRIA | SUP_LSS | L2S | SUP_SYSTEMES | UPMC | LJLL | SORBONNE-UNIVERSITE | SU-SCIENCES | UNIV-PARIS7 | USPC | SUPELEC

Citation

Jose Luis Avila Alonso, Catherine Bonnet, Emilia Fridman, Frédéric Mazenc, Jean Clairambault. Stability analysis of PDE’s modelling cell dynamics in Acute Myeloid Leukemia. 53rd IEEE Annual Conference on Decision and Control (CDC 2014), Dec 2014, Los Angeles, United States. ⟨10.1109/cdc.2014.7039860⟩. ⟨hal-01110304⟩

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