What does it mean for a mathematical model to be chaotic?

A mathematical model is considered chaotic if it exhibits sensitive dependence on initial conditions, meaning that small changes in the starting values can lead to vastly different outcomes over time. This unpredictability is often characterized by behavior that appears random, despite being governed by deterministic rules. Chaotic systems typically display patterns and structures, such as strange attractors, but do not settle into equilibrium or periodic behavior. As a result, long-term predictions become practically impossible, even though the model itself is deterministic.