Saddle-node bifurcation

The basic mechanism for the simultaneous creation and destruction of fixed points; sometimes refered to as a blue sky bifurcation because fixed points may surprisingly appear 'out of the blue sky", but also called a fold bifurcation because of the shape of the bifurcation diagram. The prototypical first-order system with a saddle-node bifurcation takes the form: x′ = r - x2.