Lyapunov Exponent — Chaotic ODEs
Two close Lorenz trajectories diverge exponentially; slope of log|δ| gives λ₁
System:
Lorenz
Rössler
Parameter σ (Lorenz) / a (Rössler):
10.0
Parameter r (Lorenz) / c (Rössler):
28.0
δ₀ initial separation:
1e-8
Reset
λ₁ = computing…
Lorenz: ẋ=σ(y-x), ẏ=rx-y-xz, ż=xy-bz
b=8/3, chaotic for r>24.74
λ₁ ≈ +0.906 (canonical Lorenz)
Negative λ → stable; positive → chaos