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.