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 56 条

[51] WAN A., 2002, KYUSHU J MATH, V56, P193
[52] Wan AY, 2004, COMPUT MATH APPL, V47, P1257, DOI [10.1016/S0898-1221(04)90120-4, 10.1016/j.camwa.2004.04.011]
[53] Global attractivity of periodic solution in a model of hematopoiesis
Weng, PX
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2002, 44 (8-9) : 1019 - 1030
[54] A necessary and sufficient condition for the existence of positive periodic solutions of a model of hematopoiesis
Wu, Xin-Min
Li, Jing-Wen
Zhou, Hou-Qing
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (06) : 840 - 849
[55] Periodic solutions for scalar functional differential equations
Ye, D
Fan, M
Wang, HY
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (07) : 1157 - 1181
[56] A new existence theory for single and multiple positive periodic solutions to Volterra integro-differential equations with impulse effects
Zhang, XY
Jiang, DQ
Li, XY
Wang, K
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 51 (01) : 17 - 32

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