Continuous flow · dim 3
Lorenz '63
Edward Lorenz's 1963 truncation of atmospheric convection. The first explicitly studied strange attractor: bounded, sensitive to initial conditions, with a fractal dimension ≈ 2.06. Origin of 'the butterfly effect'.
Equations
dx/dt = σ(y − x)
dy/dt = x(ρ − z) − y
dz/dt = xy − β zAt a glance
| Parameters | σ = 10, ρ = 28, β = 8/3 (classical) |
|---|---|
| Chaotic for | ρ > 24.74 (Hopf bifurcation), classical at ρ = 28 |
| Lyapunov exponent | λ₁ ≈ 0.906 (classical) |
| History | Lorenz, 'Deterministic Nonperiodic Flow', J. Atmos. Sci. (1963). |
Try it
Open the interactive playground at /tools/lorenz.
See also
Quick quiz
Test yourself on lorenz
8 multiple-choice questions. Pick an answer for each, then submit to see explanations.
Q1.Lorenz '63 came from truncating which physical system?
Q2.Lorenz at classical (10, 28, 8/3) has Kaplan-Yorke dimension approximately:
Q3.Hopf bifurcation in Lorenz occurs near:
Q4.Smale solved the problem of whether the Lorenz attractor is truly strange:
Q5.The two-wing structure comes from:
Q6.Lorenz observed chaos by accident in:
Q7.The Lorenz attractor exhibits which kind of symmetry?
Q8.What's the largest ρ before transient chaos disappears in Lorenz?