Sprott Strange Attractor

Simplest chaotic flow ẋ=y, ẏ=z, ż=-az+y²-x — diverging nearby trajectories

Sprott J attractor: ẋ=y, ẏ=z, ż=-az+y²-x. One of the simplest possible chaotic ODEs (Sprott 1994). Strange attractor has fractal structure; Lyapunov exponent λ₁≈0.07 for a≈2.017. Right panel: two nearby trajectories (separation δ(0)=10⁻⁸) diverge exponentially — sensitivity to initial conditions. Lyapunov exponent estimated from log[|δ(t)|/|δ(0)|]/t.