English: Dynamics of the Hopf bifurcation near ${\displaystyle \lambda =0}$. Possible trajectories in red, stable structures in dark blue and unstable structures in dashed light blue. Supercritical Hopf bifurcation: 1a) stable fixpoint 1b) instable fixpoint, stable limit cycle 1c) phase space dynamics. Subcritical Hopf bifurcation: 2a) stable fixpoint, unstable limit cycle 2b) instable fixpoint 2c) phase space dynamics. ${\displaystyle \omega }$ determines the angular dynamics and therefore the direction of winding for the trajectories.