For the constant injection system, expressions for the fixed points can be readily obtained.

Assume that a fixed point in the system can be written

Substituting this into Eqns. (45) and (40), it can be shown that the fixed points for the magnitude and phase of the laser field go as the cube root of the control parameter , as seen in Figure [8(a)].

**Figure 8:** Bifurcation diagram e vs. injection parameter b. (a) Fixed points of system. (b) Overview of various regimes. (c) Supercritical Hopf Bifurcation