Limit Sets in Semi-Dynamical Systems

Semi-dynamical systems are fundamental tools in the study of nonlinear dynamics, providing valuable insights into the long-term behavior of systems governed by continuous time evolution.Among their essential aspects, limit sets play a critical role in describing the asymptotic behavior of trajectories.This paper delves into the concept of limit sets in semi-dynamical systems, exploring their properties, classifications, and significance in various contexts.The study also introduces novel perspectives by investigating limit sets under specific conditions, such as delayed feedback, hybrid dynamics, and fractal structures, offering potential directions for future research.