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# Rabinovich-Fabrikant equations

The Rabinovich-Fabrikant equations are a set of three coupled ordinary differential equations exhibiting chaotic behavior for certain values of the parameters. The equations are:

$dot\left\{x\right\}=y\left(z-1+x^2\right)+gamma x$
$dot\left\{y\right\}=x\left(3z+1-x^2\right)+gamma y$
$dot\left\{z\right\}=-2z\left(alpha+xy\right).$

An example of chaotic behavior is obtained for $gamma=0.87$ and $alpha=1.1$. The correlation dimension was found to be 2.19 ± 0.01. (See Grassberger et al. 1983).