Gauss iterated map

In mathematics, the Gauss map (also known as Gaussian map[1] or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:

${\displaystyle x_{n+1}=\exp(-\alpha x_{n}^{2})+\beta ,\,}$

Cobweb plot of the Gauss map for ${\displaystyle \alpha =4.90}$ and ${\displaystyle \beta =-0.58}$. This shows an 8-cycle.

where α and β are real parameters.

Named after Johann Carl Friedrich Gauss, the function maps the bell shaped Gaussian function similar to the logistic map.