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

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