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

[21] Oscillation of differential equations with non-monotone retarded arguments
Chatzarakis, George E.
Ocalan, Ozkan
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2016, 19 (01): : 98 - 104
[22] On Oscillation of Differential Equations with Non-monotone Deviating Arguments
G. E. Chatzarakis
Mediterranean Journal of Mathematics, 2017, 14
[23] On Oscillation of Differential Equations with Non-monotone Deviating Arguments
Chatzarakis, G. E.
MEDITERRANEAN JOURNAL OF MATHEMATICS, 2017, 14 (02)
[24] Oscillation criteria for difference equations with non-monotone arguments
George E Chatzarakis
Leonid Shaikhet
Advances in Difference Equations, 2017
[25] Oscillation criteria for difference equations with non-monotone arguments
Chatzarakis, George E.
Shaikhet, Leonid
ADVANCES IN DIFFERENCE EQUATIONS, 2017,
[26] Oscillation of differential equations with non-monotone retarded arguments
Ocalan, Ozkan
LMS JOURNAL OF COMPUTATION AND MATHEMATICS, 2015, 18 (01): : 660 - 666
[27] PD control at Neimark-Sacker bifurcations in a Mackey-Glass system
Wang, Yuanyuan
ADVANCES IN DIFFERENCE EQUATIONS, 2018,
[28] Dual synchronization of chaos in Mackey-Glass electronic circuits with time-delayed feedback
Sano, Satoshi
Uchida, Atsushi
Yoshimori, Shigeru
Roy, Rajarshi
PHYSICAL REVIEW E, 2007, 75 (01):
[29] Mackey-Glass type delay differential equations near the boundary of absolute stability
Liz, E
Trofimchuk, E
Trofimchuk, S
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 275 (02) : 747 - 760
[30] Noise-enhanced stability in the time-delayed Mackey-Glass system
Zhang, J. Q.
Chen, R. Y.
Nie, L. R.
INDIAN JOURNAL OF PHYSICS, 2015, 89 (12) : 1321 - 1326

← 1 2 3 4 5 →