A note on global attractivity in models of hematopoiesis - Gopalsamy К. (Ukrains’kyi Matematychnyi Zhurnal, 1998)
We consider the delay differential equations \(P’(t) = β _0 θ ^n [P(t - τ )]^j θ ^n + [P(t - τ )]^n - δ P(t), j = 0,1,\) which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for the positive equilibrium of the equation considered to be a global attractor. In contrast to the Lasota-Wazewska model, we establish the existence of the number δj = δj(n, τ) > 0 such that the equilibrium of the equation under consideration is a global attractor for all δ ε (0, δj] independently of β0 and θ.