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

If the Mackey–Glass equationx˙(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 an...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 450; no. 2; pp. 1208 - 1228
Main Authors Berezansky, Leonid, Braverman, Elena
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.06.2017
Subjects
Global stability
Instability
Local stability
Mackey–Glass equation
Non-oscillatory unstable solutions
Two delays
Instability
Non-oscillatory unstable solutions
Global stability
Two delays
Mackey–Glass equation
Local stability
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Summary:If the Mackey–Glass equationx˙(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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2017.01.050