Nonlinear Dynamics: Stability and Chaos

This lecture covers the concepts of fixed point stability, focusing on the behavior of systems near equilibrium points. It discusses the conditions for stability and asymptotic stability, emphasizing the role of Lyapunov functions. The lecture also explores examples of Lotka-Volterra models for competition, illustrating the dynamics of interacting species. Additionally, it delves into the classification of fixed points based on their stability properties, such as centers, nodes, and saddles. The presentation concludes with a discussion on nonlinear dynamics, chaos, and complex systems, highlighting the importance of understanding the behavior of nonlinear systems.