Quite recently found by the electrical engineers Sara Dadras and Hamid Momeni in 2009, this attractor is special because it changes its scrollness when varying just one parameter.1 At $$c = 4.7$$, the chaotic attractor shows just two wings, at $$c = 3.9$$ it suddenly evolves four scroll-like wings and at $$c = 1.7$$ it goes back to tree scrolls. Around these values several things happen:

• $$0 < c \le 0.77$$: single stable point
• $$0.77 < c \le 1.5$$: single stable oscillation
• $$1.5 < c \le 4.45$$: chaos
• $$4.45 < c < 5.17$$: several regions of stable oscillations with chaotic outbreaks inbetween
• $$5.17 \le c < 7$$: multiple stable limit cycles

## Renders

### Three-Scroll

Differential system:

$\dot{x} = y - a\, x + b\, y\, z$ $\dot{y} = z + c\, x - x\, z$ $\dot{z} = d\, x\, y - h\, z$

Constants:

$a = 3$ $b = 2.7$ $c = 1.7$ $d = 2$ $h = 9$ ### Four-Scroll

As above, $$c = 3.9$$. 1. S. Dadras and H. R. Momeni, 2009. "A novel three-dimensional autonomous chaotic system generating two, three and four-scroll attractors". Phys. Let. A. 373(40). doi:10.1016/j.physleta.2009.07.088

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