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
收藏
页码：6268 / 6283
页数：16
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