| Contents |
| A scalar differential delay equation of the form
$$
\varepsilon x^{\,\prime}(t)+x(t)=f(x(t-1))
$$
is considered where function $f$ is a Farey-type nonlinearity defined by
$$
G(x)=\left\{\begin{array}{rl} {}&mx+A\quad\mbox{if}\quad x\le0\\
{}&mx+B\quad\mbox{if}\quad x>0
\end{array}\right.
$$
for some $0B$. The map $f$ as a dynamical system always has a unique globally attracting cycle. The problem of existence of periodic solutions of the differential delay equation and their properties in relation to the one-dimensional map $f$ are studied for small $\varepsilon>0$. Theoretical results are demonstrated and supported by numerical calculations. |
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