Given the following system dependent on the parameter $\mu$ :
\begin{equation*} \begin{cases} \dot{x}=y+(\mu-1)x-x^3 \\ \dot{y}=-x+(\mu-1)y+2x^3 \end{cases} \end{equation*}
I was asked for which values of $\mu$ are stable limit cycles present. I have found out that for $\mu=1$ there is a Hopf bifurcation, and according to the theory since the Lyapunov number is negative a stable limit cycle bifurcates from the origin for $\mu > 1$
Now I am asked to investigate the amplitude of the stable limit cycles as a function of $\mu$. But I have no clue how to do that and I cannot find anything about on any of my books. Any suggestions? :)