Coupled Map Lattice — Spatiotemporal Chaos

CML Parameters

Logistic r: 3.8 Coupling ε: 0.30 Lattice size L: 120

Equations

xᵢ(t+1) = (1−ε)f(xᵢ) + ε/2[f(xᵢ₋₁)+f(xᵢ₊₁)]

f(x) = rx(1−x) (logistic map)

λ = lim⟨ln|f'(x)|⟩ (Lyapunov)

Running...

Phases

CMLs show rich spatiotemporal behavior: frozen chaos (clusters of periodic domains), pattern selection (spatial period-2 bands), and fully developed turbulence (ε small). The Lyapunov spectrum characterizes chaotic spreading. Kaneko's 1984 model is a paradigm for extended chaos in continuous systems.