A system is considered chaotic when it exhibits sensitive dependence on initial conditions, which means that even small differences in initial conditions can lead to vastly different outcomes over time. In other words, a small change in the initial state of the system can lead to a large difference in its behavior over time.

Chaotic systems are typically deterministic, meaning that their behavior is completely determined by their initial conditions and the rules that govern their evolution. However, because the behavior of a chaotic system is so sensitive to its initial conditions, it can be difficult or impossible to predict its long-term behaviour with certainty.

Chaotic systems are found in many areas of science and engineering, including physics, biology, and economics. Some examples of chaotic systems include weather patterns, fluid dynamics, the behavior of the stock market, and the motion of planets in the solar system.