# Gauss iterated map

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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:

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 can be chaotic. The map is also called the *mouse map* because its bifurcation diagram resembles a mouse (see Figures).

## References

- ↑ Chaos and nonlinear dynamics: an introduction for scientists and engineers, by Robert C. Hilborn, 2nd Ed., Oxford, Univ. Press, New York, 2004.