Lyapunov Spectrum & Bifurcation
Logistic map xₙ₊₁ = r·xₙ·(1−xₙ) — where chaos lives
r min:
2.50
r max:
4.00
Resolution:
500
Iterations (skip):
200
Iterations (plot):
100
Recompute
λ > 0
→ chaos (red)
λ < 0
→ stable (blue)
λ = 0
→ period-doubling
Feigenbaum constant δ ≈ 4.6692
Onset of chaos: r ≈ 3.5699
Period-2: r ≈ 3.0
Period-4: r ≈ 3.449
Chaotic (λ>0)
Stable (λ<0)
λ=0 line