In
mathematics, the Gauss map (also known as Gaussian map
[Chaos 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
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form
f(x) = \exp (-x^2)
and with parametric extension
f(x) = a \exp\left( -\frac \right)
for arbitrary real constants , and non-zero . It is ...
:
:
where ''α'' and ''β'' are real parameters.
Named after
Johann Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; german: Gauß ; la, Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields in mathematics and science. Sometimes refer ...
, 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
Chaotic maps
{{chaos-stub