Rabinovich-Fabrikant Equation

The 3-D Map

$\displaystyle \dot x$	$\textstyle =$	$\displaystyle y(z-1+x^2)+\gamma x$
$\displaystyle \dot y$	$\textstyle =$	$\displaystyle x(3z+1-x^2)+\gamma y$
$\displaystyle \dot z$	$\textstyle =$	$\displaystyle -2z(\alpha+xy)$

(Rabinovich and Fabrikant 1979). The parameters are most commonly taken as $\gamma=0.87$ and $\alpha=1.1$ . It has a Correlation Exponent of $2.19\pm 0.01$ .

References

Grassberger, P. and Procaccia, I. ``Measuring the Strangeness of Strange Attractors.'' Physica D 9, 189-208, 1983.

Rabinovich, M. I. and Fabrikant, A. L. Sov. Phys. JETP 50, 311-317, 1979.