Sprott B

Sprott B — one of J. C. Sprott's simple chaotic flows (1994), realized as an analog circuit at glensstuff.com. Found by systematic search for the algebraically simplest systems that still produce chaos.

Five terms, two of them nonlinear (yz and xy). ∇·F = −1 everywhere, so a cloud of starting points loses volume at one steady rate, by a factor of e every unit of time. The equations are unchanged by (x, y, z) → (−x, −y, z), so the attractor is symmetric under a half turn about the z axis, or has a twin that is its half-turned copy.

dx/dt = yz
dy/dt = x − y
dz/dt = 1 − xy

Open Sprott B in chaosrack →

It opens running, on the model selector, with its own knobs. Rotate it by dragging, zoom with the wheel, and turn the parameters to see what the figure does when the system changes.