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
1:08:32Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators
This session differentiates between supercritical and subcritical Hopf bifurcations, illustrating their relevance in aeroelastic instabilities like airplane wing flutter and various chemical oscillation phenomena. Computer simulations are used to demonstrate these concepts.
Supercritical vs subcritical Hopf. Airplane wing vibrations. Flutter. Chemical oscillations. Computer simulations.
Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 8.2, 8.3.
Bifurcations in Two-Dimensional Systems
Next · Lecture 14Global Bifurcations of Cycles