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
1:08:32Averaging Theory for Weakly Nonlinear Oscillators
This lecture derives averaged equations for the slowly-varying amplitude and phase of weakly nonlinear oscillators. It applies these concepts to the van der Pol oscillator and the Duffing equation, yielding explicit solutions for amplitude dynamics.
Derivation of averaged equations for slowly-varying amplitude and phase. Explicit solution of amplitude equation for weakly nonlinear van der Pol oscillator. Duffing equation.
Reading: Strogatz, "Nonlinear Dynamics and Chaos", Section 7.6.