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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
Article

Abstract

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.

Keywords

Global Attractor Delay Differential Equation Positive Equilibrium Stable Steady State Discrete Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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