This differential system found by Dequan Li in 2008 is the result of a research about the scrollness of attractors and is the first one with smooth quadratic terms that produces three scrolls¹. The system is derived from the Lorenz system by generalizing it to a “fuzzy” version which was then simplified.

Renders

Differential system:

\[\dot{x} = a\, (y - x) + d\, x\, z\] \[\dot{y} = k\, x + f\, y - x\, z\] \[\dot{z} = - e\, x^2 + x\, y + c\, z\]

Constants:

\[a = 40\] \[d = 0.16\] \[k = 55\] \[f = 20\] \[e = 0.65\] \[c = 11/6\]

Stereographic Animation

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1. D. Li, 2008. "A three-scroll chaotic attractor". Phys. Let. A. 372(4). doi:10.1016/j.physleta.2007.07.045. ↩