Lyapunov Exponent

A Lyapunov exponent measures how sensitive a system is to its starting conditions. In simple terms, it quantifies how quickly nearby states diverge or converge over time. A positive Lyapunov exponent indicates chaos, meaning small differences in initial conditions grow exponentially, making long-term predictions difficult. A negative exponent suggests the system tends to settle into a steady pattern, while zero indicates neutral stability. It's a useful tool for understanding complex, dynamic systems like weather, markets, or populations, helping us grasp whether their behavior is predictable or inherently uncertain.