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 -