This is case D of the 19 most simple nonlinear dynamical systems found by J.C. Sprott. Find more details on them and the first case A here.

Renders

Differential system:

\[\dot{x} = -y\] \[\dot{y} = x + z\] \[\dot{z} = x\, z + \alpha\, y^2\]

Constants:

\[\alpha = 3\]

Stereographic Animation

You can now get a print of the Sprott attractors in my shop! Read more about it here.