TY - JOUR
T1 - Mackey-glass equation with variable coefficients
AU - Berezansky, L.
AU - Braverman, E.
N1 - Funding Information:
was applied to model white blood cells production. Here, N(t) is the density of mature cells in blood circulation, the function, rNr/(1 + N~) modeled the blood cell reproduction, the time lag *Partially supported by Israeli Ministry of Absorption. tPartially supported by the NSERC Research Grant and the AIF Research Grant. dence should be addressed.
PY - 2006/1/1
Y1 - 2006/1/1
N2 - The Mackey-Glass equation, frac(d N, d t) = frac(r (t) N (g (t)), 1 + N (g (t))γ) - b (t) N (t), is considered, with variable coefficients and a nonconstant delay. Under rather natural assumptions all solutions are positive and bounded. Persistence and extinction conditions are presented for this equation. In the case when there exists a constant positive equilibrium, local asymptotic stability of the constant solution and oscillation about this equilibrium are analyzed. The results are illustrated by numerical examples. In particular, it is demonstrated that with delay in both terms, a solution with positive initial conditions may become negative.
AB - The Mackey-Glass equation, frac(d N, d t) = frac(r (t) N (g (t)), 1 + N (g (t))γ) - b (t) N (t), is considered, with variable coefficients and a nonconstant delay. Under rather natural assumptions all solutions are positive and bounded. Persistence and extinction conditions are presented for this equation. In the case when there exists a constant positive equilibrium, local asymptotic stability of the constant solution and oscillation about this equilibrium are analyzed. The results are illustrated by numerical examples. In particular, it is demonstrated that with delay in both terms, a solution with positive initial conditions may become negative.
KW - Asymptotics
KW - Delay equations
KW - Extinction and persistence
KW - Mackey-Glass equation
KW - Oscillation
UR - http://www.scopus.com/inward/record.url?scp=33745160074&partnerID=8YFLogxK
U2 - 10.1016/j.camwa.2005.09.001
DO - 10.1016/j.camwa.2005.09.001
M3 - Article
AN - SCOPUS:33745160074
SN - 0898-1221
VL - 51
SP - 1
EP - 16
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 1
ER -