Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia

J. L. Avila; C. Bonnet; E. Fridman; F. Mazenc; J. Clairambault

doi:10.1109/CDC.2014.7039860

Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia

J. L. Avila, C. Bonnet, E. Fridman, F. Mazenc, J. Clairambault

School of Electrical Engineering

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper we perform a stability analysis of two systems of partial differential equations (PDEs) modelling cell dynamics in Acute Myeloid Leukemia. By using a Lyapunov approach, for an equilibrium point of interest, we obtain stability bounds depending on the parameters of the systems. First, we derive sufficient conditions for boundedness of solutions. Then, asymptotic stability conditions are obtained. The results are illustrated with numerical examples and simulations.

Original language	English
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3059-3064
Number of pages	6
Edition	February
ISBN (Electronic)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7039860
State	Published - 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: 15 Dec 2014 → 17 Dec 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February

Conference

Conference	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	15/12/14 → 17/12/14

All Science Journal Classification (ASJC) codes

Control and Optimization
Control and Systems Engineering
Modelling and Simulation

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1109/CDC.2014.7039860

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Avila, J. L., Bonnet, C., Fridman, E., Mazenc, F., & Clairambault, J. (2014). Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 3059-3064). Article 7039860 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7039860

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title = "Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia",

abstract = "In this paper we perform a stability analysis of two systems of partial differential equations (PDEs) modelling cell dynamics in Acute Myeloid Leukemia. By using a Lyapunov approach, for an equilibrium point of interest, we obtain stability bounds depending on the parameters of the systems. First, we derive sufficient conditions for boundedness of solutions. Then, asymptotic stability conditions are obtained. The results are illustrated with numerical examples and simulations.",

author = "Avila, {J. L.} and C. Bonnet and E. Fridman and F. Mazenc and J. Clairambault",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",

year = "2014",

doi = "10.1109/CDC.2014.7039860",

language = "الإنجليزيّة",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Avila, JL, Bonnet, C, Fridman, E, Mazenc, F & Clairambault, J 2014, Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7039860, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., pp. 3059-3064, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 15/12/14. https://doi.org/10.1109/CDC.2014.7039860

Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia. / Avila, J. L.; Bonnet, C.; Fridman, E. et al.
53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 3059-3064 7039860 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia

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AU - Bonnet, C.

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AU - Mazenc, F.

AU - Clairambault, J.

PY - 2014

Y1 - 2014

N2 - In this paper we perform a stability analysis of two systems of partial differential equations (PDEs) modelling cell dynamics in Acute Myeloid Leukemia. By using a Lyapunov approach, for an equilibrium point of interest, we obtain stability bounds depending on the parameters of the systems. First, we derive sufficient conditions for boundedness of solutions. Then, asymptotic stability conditions are obtained. The results are illustrated with numerical examples and simulations.

AB - In this paper we perform a stability analysis of two systems of partial differential equations (PDEs) modelling cell dynamics in Acute Myeloid Leukemia. By using a Lyapunov approach, for an equilibrium point of interest, we obtain stability bounds depending on the parameters of the systems. First, we derive sufficient conditions for boundedness of solutions. Then, asymptotic stability conditions are obtained. The results are illustrated with numerical examples and simulations.

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DO - 10.1109/CDC.2014.7039860

M3 - منشور من مؤتمر

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3059

EP - 3064

BT - 53rd IEEE Conference on Decision and Control,CDC 2014

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014

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ER -

Avila JL, Bonnet C, Fridman E, Mazenc F, Clairambault J. Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia. In 53rd IEEE Conference on Decision and Control,CDC 2014. February ed. Institute of Electrical and Electronics Engineers Inc. 2014. p. 3059-3064. 7039860. (Proceedings of the IEEE Conference on Decision and Control; February). doi: 10.1109/CDC.2014.7039860

Stability analysis of PDEs modelling cell dynamics in Acute Myeloid Leukemia

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