Poincaré map

A Poincaré map is a technique used in the study of complex systems, especially those involving oscillations or cycles. It simplifies the analysis by taking a "snapshot" of the system's state each time it reaches a particular point in its cycle. Imagine tracking a pendulum: instead of following its every movement, you record its position whenever it passes a specific point. Repeating this process creates a pattern or map that reveals the system's behavior over time, helping scientists understand stability, periodicity, or chaos within the system.