Abstract:
The paper considers a system of three differential equations of the following form:
\begin{align*}
\dot x_1&=a_{11}x_1+\varphi_2(x_2)+\varphi_3(x_3),
\\
\dot x_2&=a_{21}x_1+a_{22}x_2+a_{23}x_3,
\\
\dot x_3&=a_{31}x_1+a_{32}x_2+a_{33}x_3.
\end{align*}
It is established that the given system can have periodic solutions if the generalized Routh–Hurwitz conditions hold.
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