Ikeda Map Attractor

The Ikeda map models light in a nonlinear optical cavity: zₙ₊₁ = 1 + u·zₙ·exp(i·(0.4 − 6/(1+|zₙ|²))). It transitions from stable fixed points to chaos via period-doubling.

u=0.3 (fixed pt)

u=0.5 (2-cycle)

u=0.7 (4-cycle)

u=0.9 (chaos)

u=0.99 (deep chaos)

u (coupling)0.90

Points100k

Color

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Discovered by Kensuke Ikeda (1979) as a model of laser cavities with optical bistability. The strange attractor emerges above u ≈ 0.6. Lyapunov exponents transition from negative to positive at u ≈ 0.6.