MAE5790-1 Course introduction and overview
1:16:31MAE5790-2 One dimensional Systems
1:16:44MAE5790-3 Overdamped bead on a rotating hoop
1:13:12MAE5790-4 Model of an insect outbreak
1:15:16MAE5790-5 Two dimensional linear systems
1:15:20MAE5790-6 Two dimensional nonlinear systems fixed points
1:07:17MAE5790-7 Conservative Systems
1:17:13MAE5790-8 Index theory and introduction to limit cycles
1:13:55Testing for Closed Orbits
1:16:52Van der Pol Oscillator
1:05:58Averaging Theory for Weakly Nonlinear Oscillators
1:16:08Bifurcations in Two-Dimensional Systems
46:54Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators
1:07:57Global Bifurcations of Cycles
1:16:23Chaotic Waterwheel
1:14:12Waterwheel Equations and Lorenz Equations
1:12:42Chaos in the Lorenz Equations
1:16:36Strange Attractor for the Lorenz Equations
1:13:48One-Dimensional Maps
1:14:35Universal Aspects of Period Doubling
1:11:56Feigenbaum's Renormalization Analysis of Period Doubling
1:15:59Renormalization: Function Space and a Hands-On Calculation
1:08:32Global Bifurcations of Cycles
This lecture explores global bifurcations of cycles, including Hopf, saddle-node bifurcations of cycles (SNIPER), and homoclinic bifurcations. It discusses coupled oscillators, knotted cycles, and the concept of quasiperiodicity.
Hopf, saddle-node bifurcation of cycles, SNIPER, and homoclinic bifurcation. Coupled oscillators. Knotted cycles. Quasiperiodicity.
Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 8.4, 8.6.
Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators
Next · Lecture 15Chaotic Waterwheel