Gauss iterated map

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


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

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.

Properties
In the parameter real space $$x_n$$ can be chaotic. The map is also called the mouse map because its bifurcation diagram resembles a mouse (see Figures).