Radial and angular components of the semi-classical fixedpoints. (a) Radial and (b) angular components of the semi-classical fixed points. The existence and components ofthe semi-classical fixed points are functions of the two non-dimensional ratiosof the parametric pumping magnitude κ, detuning Δ,and dissipation rate γ of the system: and .Note then that all non-zero values in (a) represent not just a single fixedpoint, but a pair of antipodal fixed points. The fixed point at origin is notplotted in (b) for the obvious reason that its angular component is undefined.The colours of the plot indicate the stability: green indicates stable fixedpoints and checkered red indicates unstable fixed points. Visible in thisdiagram is a clear semi-classical threshold where the origin becomes unstable,and above which the stable semi-classical fixed points separate.