The Mackey-glass model of respiratory dynamics: Review and new results

Leonid Berezansky, Elena Braverman, Lev Idels

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Since the celebrated Mackey-Glass model of respiratory dynamics was introduced in 1977, many results on its qualitative behavior have been obtained, including oscillation, stability and chaos. The paper reviews some known properties and presents new results for more general models: equations with time-dependent parameters, several delays, a positive periodic equilibrium and distributed delays. The problems considered in the paper involve existence, positivity and permanence of solutions, oscillation and global asymptotic stability. In addition, some general approaches to the study of nonlinear nonautonomous scalar delay equations are outlined. The paper generalizes and unifies existing results and provides an outlook on further studies.

Original languageEnglish
Pages (from-to)6034-6052
Number of pages19
JournalNonlinear Analysis, Theory, Methods and Applications
Issue number16
StatePublished - 1 Nov 2012


  • Global asymptotic stability
  • Mackey-Glass equation
  • Nonlinear delay equations
  • Oscillation and nonoscillation
  • Permanence

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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