Mackey-Glass model of hematopoiesis with monotone feedback revisited

Leonid Berezansky; Elena Braverman; Lev Idels

doi:10.1016/j.amc.2012.10.052

Mackey-Glass model of hematopoiesis with monotone feedback revisited

Leonid Berezansky, Elena Braverman, Lev Idels

Department of Mathematics

Research output: Contribution to journal › Review article › peer-review

27 Scopus citations

Abstract

For the blood cell production modeldxdt=-αx(t)+^F0 ^θnθn+^xn(t-τ),we review known results. Permanence of solutions, oscillation and stability of a positive equilibrium or a positive periodic solution are analyzed for non-Autonomous generalizations of this equation, with both concentrated and distributed delays.

Original language	English
Pages (from-to)	4892-4907
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	219
Issue number	9
DOIs	https://doi.org/10.1016/j.amc.2012.10.052
State	Published - 1 Jan 2013

Keywords

Blood cell production
Global asymptotic stability
Local stability
Mackey-Glass equation
Negative feedback
Non-oscillation
Oscillation
Permanence

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2012.10.052

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title = "Mackey-Glass model of hematopoiesis with monotone feedback revisited",

abstract = "For the blood cell production modeldxdt=-αx(t)+F0 θnθn+xn(t-τ),we review known results. Permanence of solutions, oscillation and stability of a positive equilibrium or a positive periodic solution are analyzed for non-Autonomous generalizations of this equation, with both concentrated and distributed delays.",

keywords = "Blood cell production, Global asymptotic stability, Local stability, Mackey-Glass equation, Negative feedback, Non-oscillation, Oscillation, Permanence",

author = "Leonid Berezansky and Elena Braverman and Lev Idels",

note = "Funding Information: L. Berezansky is partially supported by the Israeli Ministry of Absorption , E. Braverman is partially supported by NSERC Research Grant , L. Idels is partially supported by a Grant from VIU . ",

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doi = "10.1016/j.amc.2012.10.052",

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T1 - Mackey-Glass model of hematopoiesis with monotone feedback revisited

AU - Berezansky, Leonid

AU - Braverman, Elena

AU - Idels, Lev

N1 - Funding Information: L. Berezansky is partially supported by the Israeli Ministry of Absorption , E. Braverman is partially supported by NSERC Research Grant , L. Idels is partially supported by a Grant from VIU .

PY - 2013/1/1

Y1 - 2013/1/1

N2 - For the blood cell production modeldxdt=-αx(t)+F0 θnθn+xn(t-τ),we review known results. Permanence of solutions, oscillation and stability of a positive equilibrium or a positive periodic solution are analyzed for non-Autonomous generalizations of this equation, with both concentrated and distributed delays.

AB - For the blood cell production modeldxdt=-αx(t)+F0 θnθn+xn(t-τ),we review known results. Permanence of solutions, oscillation and stability of a positive equilibrium or a positive periodic solution are analyzed for non-Autonomous generalizations of this equation, with both concentrated and distributed delays.

KW - Blood cell production

KW - Global asymptotic stability

KW - Local stability

KW - Mackey-Glass equation

KW - Negative feedback

KW - Non-oscillation

KW - Oscillation

KW - Permanence

UR - http://www.scopus.com/inward/record.url?scp=84871252053&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2012.10.052

DO - 10.1016/j.amc.2012.10.052

M3 - Review article

AN - SCOPUS:84871252053

SN - 0096-3003

VL - 219

SP - 4892

EP - 4907

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 9

ER -

Mackey-Glass model of hematopoiesis with monotone feedback revisited

Abstract

Keywords

ASJC Scopus subject areas

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