Ukrainian Mathematical Journal

, Volume 50, Issue 1, pp 3–12 | Cite as

A note on global attractivity in models of hematopoiesis

  • K. Gopalsamy
  • S. I. Trofimchuk
  • N. R. Bantsur


We consider the delay differential equations \(P'(t) = \frac{{\beta _0 \theta ^n [P(t - \tau )]^j }}{{\theta ^n + [P(t - \tau )]^n }} - \delta P(t),{\rm{ }}j = 0,1,\) 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.


Global Attractor Delay Differential Equation Positive Equilibrium Stable Steady State Discrete Dynamical System 
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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • K. Gopalsamy
    • 1
  • S. I. Trofimchuk
    • 2
  • N. R. Bantsur
    • 2
  1. 1.Institute of MathematicsFlinders UniversityAustralia
  2. 2.Institute of MathematicsUkrainian Academy of SciencesKiev

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