Limit Cycle Oscillators: Stability and Excitability

This lecture covers the concepts of limit cycle oscillators, stability, and excitability in 2D phase portraits. The instructor explains the implications of having stable fixed points and regions, the existence of unstable limit cycles, and the direction of vectors on isoclines. The lecture also delves into positive and negative feedbacks, the selection of containment zones, and the determination of fixed points' stability. Additionally, the lecture explores the relationship between excitable systems and limit cycle oscillators, using examples like the Fitz-Hugh Nagumo model. The session concludes with a discussion on the region of existence of a limit cycle and the trajectory approaching a stable limit cycle.