TY - JOUR
T1 - The Mackey-glass model of respiratory dynamics
T2 - Review and new results
AU - Berezansky, Leonid
AU - Braverman, Elena
AU - Idels, Lev
N1 - Funding Information:
The first author was partially supported by the Israeli Ministry of Absorption . The second author was partially supported by NSERC . The research of the third author was supported by a grant from VIU .
PY - 2012/11/1
Y1 - 2012/11/1
N2 - Since the celebrated Mackey-Glass model of respiratory dynamics was introduced in 1977, many results on its qualitative behavior have been obtained, including oscillation, stability and chaos. The paper reviews some known properties and presents new results for more general models: equations with time-dependent parameters, several delays, a positive periodic equilibrium and distributed delays. The problems considered in the paper involve existence, positivity and permanence of solutions, oscillation and global asymptotic stability. In addition, some general approaches to the study of nonlinear nonautonomous scalar delay equations are outlined. The paper generalizes and unifies existing results and provides an outlook on further studies.
AB - Since the celebrated Mackey-Glass model of respiratory dynamics was introduced in 1977, many results on its qualitative behavior have been obtained, including oscillation, stability and chaos. The paper reviews some known properties and presents new results for more general models: equations with time-dependent parameters, several delays, a positive periodic equilibrium and distributed delays. The problems considered in the paper involve existence, positivity and permanence of solutions, oscillation and global asymptotic stability. In addition, some general approaches to the study of nonlinear nonautonomous scalar delay equations are outlined. The paper generalizes and unifies existing results and provides an outlook on further studies.
KW - Global asymptotic stability
KW - Mackey-Glass equation
KW - Nonlinear delay equations
KW - Oscillation and nonoscillation
KW - Permanence
UR - http://www.scopus.com/inward/record.url?scp=84864647638&partnerID=8YFLogxK
U2 - 10.1016/j.na.2012.06.013
DO - 10.1016/j.na.2012.06.013
M3 - Article
AN - SCOPUS:84864647638
SN - 0362-546X
VL - 75
SP - 6034
EP - 6052
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 16
ER -