Dynamics of a Mathematical Hematopoietic Stem-Cell Population Model

DOI10.1137/18M1165086zbMath1416.34066arXiv1712.08308OpenAlexW3098559732WikidataQ64453955 ScholiaQ64453955MaRDI QIDQ5383209

Daniel C. De Souza

Publication date: 20 June 2019

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.08308

zbMATH Keywords

Lyapunov exponentstorusdelay-differential equationscanard explosionhematopoietic stem cellshematological diseases

Mathematics Subject Classification ID

Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Periodic solutions to functional-differential equations (34K13) Cell biology (92C37) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19) Complex (chaotic) behavior of solutions to functional-differential equations (34K23)

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Uses Software

• Matlab
• DDE-BIFTOOL

Cites Work

• Unnamed Item
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• Canard explosion in delay differential equations
• A mathematical model of granulopoiesis incorporating the negative feedback dynamics and kinetics of G-CSF/neutrophil binding and internalization
• Semi-discretization for time-delay systems. Stability and engineering applications.
• Stability and bifurcation analysis in hematopoietic stem cell dynamics with multiple delays
• Chasse au canard
• High frequency spikes in long period blood cell oscillations
• Dynamic hematological disease: a review
• Geometric singular perturbation theory for ordinary differential equations
• Introduction to functional differential equations
• Global stability in a delayed partial differential equation describing cellular replication
• Normal and pathological dynamics of platelets in humans
• Origins of oscillation patterns in cyclical thrombocytopenia
• On the Lambert \(w\) function
• Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
• Boundary layer phenomena for differential-delay equations with state-dependent time lags: III.
• Power spectra and dynamical invariants for delay-differential and difference equations
• Oscillations in cyclical neutropenia: new evidence based on mathematical modeling
• A mathematical model of hematopoiesis. I: Periodic chronic myelogenous leukemia
• A mathematical model of hematopoiesis. II: Cyclical neutropenia
• Periodic oscillations in leukopoiesis models with two delays
• Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations
• Approximating Lyapunov exponents and Sacker-Sell spectrum for retarded functional differential equations
• Relaxation Oscillations in a Class of Delay Differential Equations
• Stability of Linear Delay Differential Equations
• Delay induced canards in a model of high speed machining
• Deterministic Nonperiodic Flow
• Resonance Phenomena in a Scalar Delay Differential Equation with Two State-Dependent Delays
• Canard Theory and Excitability
• Numerical bifurcation analysis of delay differential equations using DDE-BIFTOOL
• Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia
• Long Period Oscillations in aG₀Model of Hematopoietic Stem Cells
• Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays
• Roots of the Transcendental Equation Associated with a Certain Difference-Differential Equation
• Elements of applied bifurcation theory

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