In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted to the equilibrium point. Finally, some examples are presented to support the results.
Büyükkahraman, Mehtap Lafci
(R1888) On the Mackey-Glass Model with a Piecewise Constant Argument,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
2, Article 19.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss2/19