Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays

DOI10.1051/mmnp:2008001zbMath1337.34074OpenAlexW2121746227MaRDI QIDQ5744779

Fabien Crauste, Mostafa Adimy, Abderrahim El Abdllaoui

Publication date: 19 February 2016

Published in: Mathematical Modelling of Natural Phenomena (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1051/mmnp:2008001

zbMATH Keywords

Lyapunov functionalglobal and local asymptotic stabilityhematopoiesis modellingsystem of delay equations

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Stability theory of functional-differential equations (34K20) Stability of solutions to ordinary differential equations (34D20) Cell biology (92C37) Functional-differential equations (including equations with delayed, advanced or state-dependent argument) (34K99)

Related Items (13)

DISCRETE MATURITY AND DELAY DIFFERENTIAL-DIFFERENCE MODEL OF HEMATOPOIETIC CELL DYNAMICS WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA ⋮ Stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays ⋮ The ISS framework for time-delay systems: a survey ⋮ Blood Cell Dynamics: Half of a Century of Modelling ⋮ Influence of the second delay on local dynamics ⋮ A mathematical model of multistage hematopoietic cell lineages ⋮ Dynamics of a Mathematical Hematopoietic Stem-Cell Population Model ⋮ Local dynamics of an equation with two large different-order delays ⋮ Boundedness and Lyapunov function for a nonlinear system of hematopoietic stem cell dynamics ⋮ Asymptotic behavior and stability switch for a mature-immature model of cell differentiation ⋮ Adding self-renewal in committed erythroid progenitors improves the biological relevance of a mathematical model of erythropoiesis ⋮ DISCRETE-MATURITY STRUCTURED MODEL OF CELL DIFFERENTIATION WITH APPLICATIONS TO ACUTE MYELOGENOUS LEUKEMIA ⋮ Polynomial stability of the wave equation with distributed delay term on the dynamical control

Uses Software

• dde23

Cites Work

• Unnamed Item
• A new criterion for the global stability of simultaneous cell replication and maturation processes
• Introduction to functional differential equations
• Global stability in a delayed partial differential equation describing cellular replication
• Global stability of a partial differential equation with distributed delay due to cellular replication
• A nonlinear age and maturity structured model of population dynamics. II: Chaos
• A nonlinear age and maturity structured model of population dynamics. I: Basic theory
• Stability and Hopf bifurcation in a mathematical model of pluripotent stem cell dynamics
• Asymptotic behavior of a singular transport equation modelling cell division
• Geometric Stability Switch Criteria in Delay Differential Systems with Delay Dependent Parameters
• A Mathematical Study of the Hematopoiesis Process with Applications to Chronic Myelogenous Leukemia
• Long Period Oscillations in aG₀Model of Hematopoietic Stem Cells
• Roots of the Transcendental Equation Associated with a Certain Difference-Differential Equation
• Solving DDEs in Matlab

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