Gauss iterated map

Image:Gauss alpha=4.9 beta=-0.58 cobweb.png of the Gauss map for $\backslash alpha=4.90$ and $\backslash beta=-0.58$. This shows an 8-cycle.]]

In mathematics, the Gauss map (also known as Gaussian mapChaos and nonlinear dynamics: an introduction for scientists and engineers, by Robert C. Hilborn, 2nd Ed., Oxford, Univ. Press, New York, 2004. or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:

: $x\_\{n+1\}\; =\; \backslash exp(-\backslash alpha\; x^2\_n)+\backslash beta,\; \backslash ,$

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.