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

Jose Luis Avila Alonso; Catherine Bonnet; Emilia Fridman; Frédéric Mazenc; Jean Clairambault

doi:10.1109/cdc.2014.7039860

Conference papers

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.

Document type :

Conference papers

Domain :

Computer Science [cs] / Automatic Control Engineering

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https://hal.inria.fr/hal-01110304
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Submitted on : Tuesday, January 27, 2015 - 7:03:00 PM
Last modification on : Wednesday, January 12, 2022 - 3:47:26 AM

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

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