saddle: transcritical: supercritical pitchfork: subcritical pitchfork:

This Demonstration shows bifurcations of these nonlinear first-order ODEs as you vary the parameter .

The top figure shows the phase portrait, versus , with stable fixed points indicated by solid disks and unstable fixed points as open circles. The bottom figure shows the solutions, versus , starting from a number of initial states with stable fixed points indicated by solid lines and unstable fixed points as dashed lines. You can vary both the number of initial states and time duration, . Note how the fixed points and solutions change as bifurcations occur as you vary the parameter .