TY - JOUR
T1 - Mackey-Glass model of hematopoiesis with non-monotone feedback
T2 - Stability, oscillation and control
AU - Berezansky, Leonid
AU - Braverman, Elena
AU - Idels, Lev
N1 - Funding Information:
L. Berezansky is partially supported by the Israeli Ministry of Absorption, E. Braverman (corresponding author) is partially supported by NSERC Research grant , L. Idels is partially supported by a grant from VIU .
PY - 2013/1/31
Y1 - 2013/1/31
N2 - For the blood cell production model with a unimodal (hump) feedback function dy/dt=-γy(t)+βθny(t-τ) /θn+yn(t-τ),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.
AB - For the blood cell production model with a unimodal (hump) feedback function dy/dt=-γy(t)+βθny(t-τ) /θn+yn(t-τ),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.
KW - Blood cell production
KW - Control and stabilization
KW - Local and global asymptotic stability
KW - Mackey-Glass equation
KW - Non-autonomous models
KW - Non-monotone feedback
KW - Non-oscillation
KW - Permanence
UR - http://www.scopus.com/inward/record.url?scp=84872933265&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2012.12.043
DO - 10.1016/j.amc.2012.12.043
M3 - Review article
AN - SCOPUS:84872933265
SN - 0096-3003
VL - 219
SP - 6268
EP - 6283
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
IS - 11
ER -