Limit Cycle

Limit cycles, persistent periodic oscillations in dynamical systems, are a focus of intense research across diverse fields. Current investigations explore their stability and control using techniques like pseudospectra analysis, data-driven methods such as autoencoders and optimization algorithms tailored to specific system architectures (e.g., neural networks, robotic models). Understanding and manipulating limit cycles is crucial for applications ranging from stabilizing robotic locomotion and controlling machine learning algorithms to modeling biological systems and improving the performance of optimization methods in high-dimensional spaces.