Gauss iterated map

Cobweb plot of the Gauss map for and . This shows an 8-cycle.

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

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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).


Bifurcation diagram of the Gauss map with and in the range −1 to +1. This graph resembles a mouse.
Bifurcation diagram of the Gauss map with and in the range −1 to +1.

References

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