Chaos Theory
The study of deterministic non-linear dynamical systems that exhibit extreme sensitivity to initial conditions (the butterfly effect).
Governing formula
Lyapunov Exponent: δx(t) ≈ δx₀ e^(λ t), λ > 0
SI unit
Divergence Rate λ (s⁻¹)
In depth
In chaotic systems, tiny differences in initial conditions diverge exponentially over time (positive Lyapunov exponent λ > 0), rendering long-term deterministic forecasting impossible despite fully deterministic underlying equations.
Examples in the real world
Atmospheric weather forecasting models, double pendulum motion, and the Lorenz strange attractor.