Lyapunov Spectrum
Lyapunov exponent vs parameter alongside the bifurcation diagram
Map Selection
Map:
Logistic: rx(1-x)
Tent map
Sine: r·sin(πx)/π
Parameter range:
r min:
2.5
r max:
4.0
Iterations N:
500
Compute
At hover/cursor
r:
—
λ:
—
Behavior:
—
About
Lyapunov exponent λ = lim (1/n)Σ ln|f'(xᵢ)|. λ<0: stable periodic, λ=0: bifurcation point, λ>0: chaos. For logistic map at r=4: λ=ln2≈0.693. Period-doubling bifurcations occur at Feigenbaum's universal sequence with ratio δ≈4.669.