Zaslavskii map

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The Zaslavskii map is a discrete-time dynamical system. 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:

$x_{n+1}=[x_n+\nu(1+\mu y_n)+\epsilon\nu\mu\cos(2\pi x_n)]\, (\textrm{mod}\,1)$

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

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.

[edit] References

G.M. Zaslavskii (1978). "The Simplest case of a strange attractor". Phys. Lett. A 69 (3): 145–238. doi:10.1016/0375-9601(78)90195-0. (LINK)
D.A. Russel, J.D. Hanson, and E. Ott (1980). "Dimension of strange attractors". Phys. Rev. 45: 1175. (LINK)
P. Grassberger and I. Procaccia (1983). "Measuring the strangeness of strange attractors". Physica 9D: 189–208. (LINK)