Duffing's Strange Attractor

Plate 82 speaks for itself: “Pushed in rhythm, it answers in chaos.”

The Physics

A damped oscillator with a cubic spring, driven periodically, can settle onto a strange attractor. Sampled once per drive period, its motion traces a fractal Poincaré section.

x″ + 0.05 x′ + x³ = 7.5 cos t

• x: displacement (dimensionless units)
• x′, x″: first and second time derivatives
• t: dimensionless time

Ueda's parameters. The Poincaré section is a fractal.

Sources

• Y. Ueda, J. Stat. Phys. 20, 181 (1979).

On the poster

Plate 082, “Duffing's Strange Attractor”: the pixel-art plate with its slogan “Pushed in rhythm, it answers in chaos.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.