Fig. 2: An input power scan of Eq. (4) for detuning θ = 3.85.

The scan runs from right to left with the previous end iteration used as the initial condition for the next input value. The solid lines show the natural circulating evolutions, with indicative shading, while the dashed lines show unstable states. Note that the solid line has four distinct regions with shaded backgrounds. Region (1) has full symmetry where all fields have equal intensity; region (2) begins with a symmetry breaking pitchfork bifurcation and results in two asymmetric pairs of symmetric fields; region (3) begins with a second symmetry breaking pitchfork bifurcation, leading to four entirely asymmetric fields, and finally region (4) begins with a partial-symmetry restoring pitchfork bifurcation, leading to a single pair of symmetric fields, with the remaining two fields being both asymmetric to each other and to the symmetric pair.