Nonlinear Systems: Phase Portrait Analysis

This lecture covers the analysis of nonlinear systems through the study of phase portraits in 2D. It includes topics such as vector fields, isoclines, and trajectories, providing insights into the behavior of bistable regions and fixed points. The instructor explains the characterization of trajectories and the representation of velocity vectors in the phase plane, emphasizing the importance of understanding decoupled systems and the uniqueness of solutions. The lecture also delves into the explicit solution of decoupled systems and the interpretation of trajectories in the context of dynamic behavior.