Topics in Dynamical Systems: Fixed Points, Linearization, Invariant Manifolds, Bifurcations & Chaos

This video provides a high-level overview of dynamical systems, which describe the changing world around us. Topics include nonlinear dynamics, linearization at fixed points, eigenvalues and eigenvectors, bifurcations, invariant manifolds, and chaos!! @eigensteve on Twitter eigensteve.com databookuw.com This video was produced at the University of Washington %%% CHAPTERS %%% 0:00 Introduction 4:35 Linearization at a Fixed Point 9:37 Why We Linearize: Eigenvalues and Eigenvectors 14:46 Nonlinear Example: The Duffing Equation 19:59 Stable and Unstable Manifolds 21:12 Bifurcations 25:20 Discrete-Time Dynamics: Population Dynamics 27:02 Integrating Dynamical System Trajectories 29:07 Chaos and Mixing