A note on stability of Mackey–Glass equations with two delays

Leonid Berezansky, Elena Braverman

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

If the Mackey–Glass equation x˙(t)=r(t)[ax(h(t))1+xν(g(t))−x(t)] with a>1 and ν>0 incorporates not one but two variable delays, some new phenomena arise: there may exist non-oscillatory about the positive equilibrium unstable solutions, the effect of possible absolute stability for certain a and ν disappears. We obtain sufficient conditions for local and global stability of the positive equilibrium and illustrate the stability tests, as well as new effects of two different delays, with examples.

Original languageEnglish
Pages (from-to)1208-1228
Number of pages21
JournalJournal of Mathematical Analysis and Applications
Volume450
Issue number2
DOIs
StatePublished - 15 Jun 2017

Keywords

  • Global stability
  • Instability
  • Local stability
  • Mackey–Glass equation
  • Non-oscillatory unstable solutions
  • Two delays

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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