### Bazykin's model

Let us consider the Bazykin's prey-predator model [Bazykin (1998), Kuznetsov (2004)]:

\begin{equation*}
\begin{cases}
\dot{x}_1 = x_1 - \dfrac{x_1 x_2}{1 + \alpha x_1} - \varepsilon x_1^2 \\
\dot{x}_2 = -\gamma x_2 + \dfrac{x_1 x_2}{1 + \alpha x_1} - \delta x_2^2
\end{cases},
\end{equation*}

with \(\gamma = 1\) and \(\varepsilon = 0.1\).
You can visualize its phase portrait in the plane and on the Poincaré sphere: choose a value for \(\alpha\) and \(\delta\) (decimal numbers between \(0\) and \(1\)).