The control space is divided in two areas by a black line which turns round and goes back. This line is called the bifurcation set. It is the set of critical points in the control space. The two areas are made of regular points. In the neighbourhood of a regular point, the shape of the potential don't change, that is the number of its minima and maximum is constant.
Critical points are points in which one maximum and one minimum meet together to disappear.
They are the points of control space where the system state jumps. In this point, the two mimima and the maximum are merged. See this new design . Now, you may read the applet source code, if you want. In fact, the enigmatic being was here the same as the model.