Van der Pol Mathieu
The Van der Pol Mathieu equation is
\[
\begin{align*}
&\dot{x}_1 = x_2\\
&\dot{x}_2 = (k_1 - k_2x_1^2)x_2 - (w_0^2 + 2\mu u^2 - \mu)x_1 + uk_3,
\end{align*}
\]
where \(k_1 = 2, k_2 = 2, k_3 = 1, w_0 = 1\). The parameter \(u\) is designed to adjust both the parametric excitation \((2 \mu u^2)x_1\) and the external external excitation \(uk_3\).