2.I.2A

Find the fixed points of the difference equation

$u_{n+1}=\lambda u_{n}\left(1-u_{n}^{2}\right)$

Show that a stable fixed point exists when $-1<\lambda<1$ and also when $1<\lambda<2$.

*Typos? Please submit corrections to this page on GitHub.*

2.I.2A

Find the fixed points of the difference equation

$u_{n+1}=\lambda u_{n}\left(1-u_{n}^{2}\right)$

Show that a stable fixed point exists when $-1<\lambda<1$ and also when $1<\lambda<2$.