Analysis of Phase Portraits in 2D Systems

This lecture delves into the analysis of phase portraits in 2D systems, exploring the propagation of solutions between fixed points and the impact of different values of parameters. The instructor discusses the concept of potential and its role in understanding the behavior of solutions. By examining various scenarios with different parameter values, the lecture illustrates how the system's dynamics change, leading to different types of trajectories and stability properties. The lecture emphasizes the importance of choosing the right parameter values to observe specific behaviors in the system, such as the existence of connecting orbits between fixed points. Through numerical simulations and graphical representations, students gain insights into the complex dynamics of 2D systems and the significance of phase portraits in understanding biological phenomena.