Hyperbolic Fixed Points - Dynamical Systems | Lecture 16

In this lecture we continue with our analysis of nonlinear planar dynamical systems. Here we focus on fixed points and show through a Taylor expansion that their stability can be understood through a corresponding linear planar system. We introduce the concept of a hyperbolic fixed point and show how the Hartman-Grobman theorem helps us to sketch the phase plane about hyperbolic equilibria. We also show what can go wrong if a fixed point fails to be hyperbolic. This course is taught by Jason Bramburger for Concordia University. More information on the instructor: https://hybrid.concordia.ca/jbrambur/ Follow @jbramburger7 on Twitter for updates.