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 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.