STABILITY AND HOPE BIFURCATION FOR A CELL POPULATION MODEL WITH STATE-DEPENDENT DELAY

STABILITY AND HOPE BIFURCATION FOR A CELL POPULATION MODEL WITH STATE-DEPENDENT DELAY

We propose a mathematical model describing the dynamics of a hematopoietic stem cell population. The method of characteristics reduces the age-structured model to a system of differential equations with a state-dependent delay. A detailed stability analysis is performed. A sufficient condition for t...

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Veröffentlicht in:SIAM journal on applied mathematics 2009-01, Vol.70 (5), p.1611-1633
Hauptverfasser: ADIMY, MOSTAFA, CRAUSTE, FABIEN, HBID, MY LHASSAN, QESMI, REDOUANE
Format: Artikel
Sprache:eng
Schlagworte:
Cell cycle
Differential equations
Eigenvalues
Hematopoietic stem cells
Mathematical independent variables
Mathematical models
Method of characteristics
Population dynamics
Stem cells
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container_issue 5
container_start_page 1611
container_title SIAM journal on applied mathematics
container_volume 70
creator ADIMY, MOSTAFA
CRAUSTE, FABIEN
HBID, MY LHASSAN
QESMI, REDOUANE
description We propose a mathematical model describing the dynamics of a hematopoietic stem cell population. The method of characteristics reduces the age-structured model to a system of differential equations with a state-dependent delay. A detailed stability analysis is performed. A sufficient condition for the global asymptotic stability of the trivial steady state is obtained using a Lyapunov-Razumikhin function. A unique positive steady state is shown to appear through a transcritical bifurcation of the trivial steady state. The analysis of the positive steady state behavior, through the study of a first order exponential polynomial characteristic equation, concludes the existence of a Hopf bifurcation and gives criteria for stability switches. A numerical analysis confirms the results and stresses the role of each parameter involved in the system on the stability of the positive steady state.
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The method of characteristics reduces the age-structured model to a system of differential equations with a state-dependent delay. A detailed stability analysis is performed. A sufficient condition for the global asymptotic stability of the trivial steady state is obtained using a Lyapunov-Razumikhin function. A unique positive steady state is shown to appear through a transcritical bifurcation of the trivial steady state. The analysis of the positive steady state behavior, through the study of a first order exponential polynomial characteristic equation, concludes the existence of a Hopf bifurcation and gives criteria for stability switches. A numerical analysis confirms the results and stresses the role of each parameter involved in the system on the stability of the positive steady state.</abstract><pub>Society for Industrial and Applied Mathematics</pub></addata></record>
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source Jstor Complete Legacy; LOCUS - SIAM's Online Journal Archive; JSTOR Mathematics & Statistics
subjects Cell cycle
Differential equations
Eigenvalues
Hematopoietic stem cells
Mathematical independent variables
Mathematical models
Method of characteristics
Population dynamics
Stem cells
title STABILITY AND HOPE BIFURCATION FOR A CELL POPULATION MODEL WITH STATE-DEPENDENT DELAY
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