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Chaos Theory

★★★★☆Undergraduate

📖Definition

Chaos is unpredictable behavior in deterministic systems. It shows extreme sensitivity to initial conditions (butterfly effect), making long-term prediction impossible.

📐Formulas

x_n+1 = rxₙ(1 - xₙ)

Logistic map (classic chaos example)

λ = lim_n → ∈fty (1)/(n) ∑_i=0^n-1 ln|f'(xᵢ)|

Lyapunov exponent

✏️Examples

예제 1

Explain why logistic map with r = 4 is chaotic.

📜History

Discovered by: Edward Lorenz (1963)

Meteorologist Lorenz discovered sensitivity to initial conditions in weather models, initiating chaos theory.

⚡Applications

Meteorology

Weather prediction limits

Cryptography

Chaos-based encryption

Ecology

Population fluctuations

🔗Related Documents

#카오스#나비효과#chaos#butterfly effect