Maximal Lyapunov Functions

Maximal Lyapunov Functions are tools used in mathematics and engineering to analyze the stability of dynamic systems. In simple terms, they help determine whether a system will return to a stable state after being disturbed. A maximal Lyapunov function is the largest function that indicates the system's stability, showing how disturbances affect its behavior. If this function decreases over time, it suggests that the system is stable and will eventually settle down. Researchers use these functions to ensure that systems, like robots or ecosystems, can reliably reach and maintain balance despite changes or disruptions.