Mackey-Glass model of hematopoiesis with non-monotone feedback: Stability, oscillation and control

Leonid Berezansky, Elena Braverman, Lev Idels

Research output: Contribution to journalReview articlepeer-review

38 Scopus citations

Abstract

For the blood cell production model with a unimodal (hump) feedback function dy/dt=-γy(t)+βθny(t-τ) /θn+yn(t-τ),we review the known results and investigate generalizations of this equation. Permanence, oscillation and stability of the positive equilibrium are studied for non-autonomous equations, including equations with a distributed delay. In addition, a linear control is introduced, and possibilities to stabilize an otherwise unstable positive equilibrium are explored.

Original languageEnglish
Pages (from-to)6268-6283
Number of pages16
JournalApplied Mathematics and Computation
Volume219
Issue number11
DOIs
StatePublished - 31 Jan 2013

Keywords

  • Blood cell production
  • Control and stabilization
  • Local and global asymptotic stability
  • Mackey-Glass equation
  • Non-autonomous models
  • Non-monotone feedback
  • Non-oscillation
  • Permanence

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