Lyapunov Spectrum of Coupled Maps

Coupled logistic maps: xᵢ(t+1) = (1−ε)f(xᵢ) + ε/2·[f(xᵢ₋₁)+f(xᵢ₊₁)]. The Lyapunov spectrum {λ₁≥λ₂≥…≥λₙ} characterizes chaos. When coupling ε increases past a threshold, synchronization occurs: λ₁>0 but transverse exponents go negative, collapsing all trajectories onto a synchronized manifold.