Gauss iterated map - Alchetron, The Free Social Encyclopedia

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 ⁡ ( − α x n 2 ) + β ,

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).

References

Gauss iterated map Wikipedia

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