A global mathematical investigation of a predator-prey model

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