Local and global bifurcation for \(\ \dot{x} =1-y^2,\ \dot{y}=-x-\mu y - y^2\)

Move the slider below to change the value of \(\mu\). The two red dots, localted at \((\mu-1,-1)\) and \((-\mu-1,1)\), are fixed point. The fixed point \( (-\mu-1,1)\) is always a saddle, but the fixed point \((\mu-1,-1)\) changes from a unstable focus to a stable focus as \(\mu\) increases beyond \(2\). There is one global bifurcation point at around \(\mu=1.63\), when a limit cycle emerges.