Halvorsen's Cyclically Symmetric Attractor

25 Jun 2021


The Halvorsen attractor is described by the following ODEs

x˙=αx4y4zy2y˙=αy4z4xz2z˙=αz4x4yx2\begin{align*}\dot{x}&=-\alpha x - 4y - 4z - y^2\\\dot{y}&=-\alpha y - 4z - 4x - z^2\\\dot{z}&=-\alpha z - 4x - 4y - x^2\end{align*}

In the above demo, α=1.89.\alpha = 1.89.