Zaslavskii map

File:Zaslavskii map.png

Zaslavskii map with parameters: $ϵ=5,\nu =0.2,r=2.$

The Zaslavskii map is a discrete-time dynamical system introduced by George M. Zaslavsky. It is an example of a dynamical system that exhibits chaotic behavior. The Zaslavskii map takes a point ($x_n,y_n$) in the plane and maps it to a new point:

$x_{n+1}=[x_n+\nu (1+\mu y_n)+ϵ\nu \mu \cos (2\pi x_n)](\text{<mrow data-mjx-texclass="ORD">mod</mrow>}1)$

$y_{n+1}=e^{-r}(y_n+ϵ\cos (2\pi x_n))$

and

$\mu =\frac{1-e^{-r}}{r}$

where mod is the modulo operator with real arguments. The map depends on four constants ν, μ, ε and r. Russel (1980) gives a Hausdorff dimension of 1.39 but Grassberger (1983) questions this value based on their difficulties measuring the correlation dimension.

See also

• List of chaotic maps

References

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