  The existence of periodic solutions is proven for some neuroscience models
with a small parameter. Moreover, the stability of such solutions is
investigated, as well. The results are based on a theoretical research dealing
with the functional differential equation with parameters $$ \dot{x}(t)=L(\tau)
x_t + \varepsilon f(t, x_t), $$ where $L: \mathbb{R}_+\rightarrow
\mathcal{L}(C; \mathbb{R})$ and $f: \mathbb{R} \times C \rightarrow \mathbb{R}$
are, respectively, linear and nonlinear operators, and $\varepsilon>0$ is a
small enough parameter. The theoretical results are applied to a Parkinson's
disease model, where the obtained conclusions are illustrated by numerical
simulations.
