A representative <normal form> for a <saddle-node bifurcation> of a map is $\boxed{x_{n+1}=x_n+\mu-x_n^2}$. Two fixed points $x=\pm\sqrt\mu$ appear for $\mu>0$; near the bifurcation the positive branch is stable and the negative branch unstable.

Solution

Past exam of the mathematics course of the University of Cambridge / 2008 / ii / Paper 3 / 7A / i / Solution

 Solution (source code)