A note on stability of Mackey Glass equations with two delays

作者：Berezansky Leonid; Braverman Elena^*

来源：Journal of Mathematical Analysis and Applications, 2017, 450(2): 1208-1228.

DOI：10.1016/j.jmaa.2017.01.050

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

If the Mackey-Glass equation
(x)over dot = r(t) [ax(h(t))/1+x(v) (g(t)) - x(t)]
with a > 1 and v > 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 v 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.

• 出版日期2017-6-15