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| [[Image:Gauss alpha=4.9 beta=-0.58 cobweb.png|thumb|right|300px|Cobweb plot of the Gauss map for <math>\alpha=4.90</math> and <math>\beta=-0.58</math>. This shows an 8-cycle.]]
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| In [[mathematics]], the '''Gauss map''' (also known as '''Gaussian map'''<ref>Chaos and nonlinear dynamics: an introduction for scientists and engineers, by Robert C. Hilborn, 2nd Ed., Oxford, Univ. Press, New York, 2004.</ref> or '''mouse map'''), is a nonlinear iterated map of the [[Real number|reals]] into a real interval given by the [[Gaussian function]]:
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| : <math> x_{n+1} = \exp(-\alpha x^2_n)+\beta, \, </math>
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| where ''α'' and ''β'' are real parameters.
| | Knowing how to evaluate the [https://www.vocabulary.com/dictionary/strength strength] or the office of a reputable lawyer can help you get the best possible [https://www.Google.com/search?hl=en&gl=us&tbm=nws&q=outcome&btnI=lucky outcome] in court For more on [http://durl.me/7mbkhp affordable Defense attorney] visit our own webpage. . |
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| Named after [[Carl Friedrich Gauss|Johann Carl Friedrich Gauss]], the function maps the bell shaped Gaussian function similar to the [[logistic map]].
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| ==Properties==
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| In the parameter real space <math>x_n</math> can be chaotic. The map is also called the ''mouse map'' because its [[bifurcation diagram]] resembles a [[mouse]] (see Figures).
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| {|
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| |[[Image:Gauss Orbit Map alpha=4.9.png|thumb|300px|Bifurcation diagram of the Gauss map with <math>\alpha=4.90</math> and <math>\beta</math> in the range −1 to +1. This graph resembles a mouse.]]
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| |[[Image:Gauss Orbit Map alpha=6.2.png|thumb|300px|Bifurcation diagram of the Gauss map with <math>\alpha=6.20</math> and <math>\beta</math> in the range −1 to +1.]]
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| |}
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| ==References== | |
| <references>
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| </references>
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| {{DEFAULTSORT:Gauss Iterated Map}}
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| [[Category:Chaotic maps]] | |
Latest revision as of 22:49, 13 May 2014
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