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
1:08:32Strange Attractor for the Lorenz Equations
This session defines attractors, chaos, and strange attractors, exploring the dynamics on the Lorenz attractor. It introduces the Lorenz map for reduction to a 1-D system and uses cobweb diagrams to rule out stable limit cycles for specific parameters.
Defining attractor, chaos, and strange attractor. Transient chaos in games of chance. Dynamics on the Lorenz attractor. Reduction to a 1-D map: the Lorenz map. Ruling out stable limit cycles for the Lorenz system when r = 28. Cobweb diagrams.
Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 9.3, 9.4.