Dynamics of a predator-prey model

We construct a global bifurcation diagram of the plane differential system
$$
\begin{array}{l} \dot x=x(1-x)-xy/(a+x^2),\\ \dot y=y(\delta-\beta y/x),\\ x(t)>0,\, y(t)>0,\, a>0,\,\delta>0,\,\beta>0, \end{array}
$$
which describes the predator-prey interaction.