$ dx/dt=\mu x+y+x^2+x^3 , dy/dt=-x+\mu y+x^2y$
What I have done so far is getting the matrix A with $A_{11}=\mu,A_{12}=1,A_{21}=-1,A_{22}=\mu$ at $(0,0)$.I can see the bifurcation is Hopf bifurcation.But I'm not sure whether it is subcritical or degenerate?At origin,a stable spiral becomes to an unstable spiral as $\mu$ changes from negative to positive.(Thus it's not supercritical.) Can someone help me to solve this problem?
I know by phase portrait I can see it's a subcritical hopf bifurcation.But is there any proof to show that?I thought about change coordinate to polar,but I'm stuck at the middle of the calculation.