Mackey-Glass model of hematopoiesis with non-monotone feedback: Stability, oscillation and control

被引：41

作者：

Berezansky, Leonid ^{[1
]}

Braverman, Elena ^{[2
]}

Idels, Lev ^{[3
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[2] Univ Calgary, Dept Math & Stats, Calgary, AB T2N 1N4, Canada

[3] VIU, Dept Math, Nanaimo, BC V9S 5J5, Canada

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 11期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Mackey-Glass equation; Non-monotone feedback; Control and stabilization; Local and global asymptotic stability; Non-autonomous models; Permanence; Non-oscillation; Blood cell production; DELAY-DIFFERENTIAL EQUATIONS; POSITIVE PERIODIC-SOLUTIONS; GLOBAL ATTRACTIVITY; DEPENDENT STABILITY; EXISTENCE THEORY; CHAOTIC SYSTEMS; POPULATION; ABSOLUTE; DYNAMICS;

D O I：

10.1016/j.amc.2012.12.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the blood cell production model with a unimodal (hump) feedback function dy/dt = -gamma y(t) + beta theta(n)y(t - tau)/theta(n) + y(n) (t -tau ) we review the known results and investigate generalizations of this equation. Permanence, oscillation and stability of the positive equilibrium are studied for non- autonomous equations, including equations with a distributed delay. In addition, a linear control is introduced, and possibilities to stabilize an otherwise unstable positive equilibrium are explored. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：6268 / 6283

页数：16

共 50 条

[1] Mackey-Glass model of hematopoiesis with monotone feedback revisited
Berezansky, Leonid
Braverman, Elena
Idels, Lev
APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (09) : 4892 - 4907
[2] MODIFIED MACKEY-GLASS MODEL OF RESPIRATION CONTROL
LANDA, PS
ROSENBLUM, MG
PHYSICAL REVIEW E, 1995, 52 (01): : R36 - R39
[3] Global exponential stability for the Mackey-Glass model of respiratory dynamics with a control term
Wang Wentao
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2016, 39 (03) : 606 - 613
[4] On periodic solutions of Mackey-Glass hematopoiesis model via concave and increasing operator
Yao, Zhijian
Alzabut, Jehad
Obaidat, Saleem
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2022, (47): : 1048 - 1058
[5] Bifurcation analysis of Mackey-Glass electronic circuits model with delayed feedback
Wan, Aying
Wei, Junjie
NONLINEAR DYNAMICS, 2009, 57 (1-2) : 85 - 96
[6] Numerical bifurcation control of Mackey-Glass system
Su, Huan
Ding, Xiaohua
Li, Wenxue
APPLIED MATHEMATICAL MODELLING, 2011, 35 (07) : 3460 - 3472
[7] On the Mackey-Glass Model with Piecewise Constant Argument
Buyukkahraman, Mehtap Lafci
APPLICATIONS AND APPLIED MATHEMATICS-AN INTERNATIONAL JOURNAL, 2022, 17 (02): : 601 - 612
[8] Chaos synchronization in the multifeedback Mackey-Glass model
Shahverdiev, EM
Nuriev, RA
Hashimova, LH
Huseynova, EM
Hashimov, RH
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2005, 19 (23): : 3613 - 3618
[9] A relay Mackey-Glass model with two delays
Preobrazhenskaya, M. M.
THEORETICAL AND MATHEMATICAL PHYSICS, 2020, 203 (01) : 524 - 534
[10] Stability and bifurcation of a numerical discretization Mackey-Glass system
Ding, Xiaohua
Fan, Dejun
Liu, Mingzhu
CHAOS SOLITONS & FRACTALS, 2007, 34 (02) : 383 - 393

← 1 2 3 4 5 →