Sprott S

Sprott S — 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.

Six terms, one of them nonlinear (z²). ∇·F = −1 everywhere, so a cloud of starting points loses volume at one steady rate, by a factor of e every unit of time.

dx/dt = −x − 4y
dy/dt = x + z²
dz/dt = 1 + x

Open Sprott S 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.