Nonlinear Dynamics and Chaos
About Course
This course provides an introduction to nonlinear dynamics and chaos. It covers analytic and geometric methods for analyzing systems of differential equations and maps, with applications to physics, biology, and engineering.
Course Content
Nonlinear Dynamics and Chaos
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MAE5790-1 Course introduction and overview
01:16:31 -
MAE5790-2 One dimensional Systems
01:16:44 -
MAE5790-3 Overdamped bead on a rotating hoop
01:13:12 -
MAE5790-4 Model of an insect outbreak
01:15:16 -
MAE5790-5 Two dimensional linear systems
01:15:20 -
MAE5790-6 Two dimensional nonlinear systems fixed points
01:07:17 -
MAE5790-7 Conservative Systems
01:17:13 -
MAE5790-8 Index theory and introduction to limit cycles
01:13:55 -
MAE5790-9 Testing for closed orbits
01:16:52 -
MAE5790-10 van der Pol oscillator
01:05:57 -
MAE5790-11 Averaging theory for weakly nonlinear oscillators
01:16:08 -
MAE5790-12 Bifurcations in two dimensional systems
46:54 -
MAE5790-13 Hopf bifurcations in aeroelastic instabilities and chemical oscillators
01:07:57 -
MAE5790-14 Global bifurcations of cycles
01:16:22 -
MAE5790-15 Chaotic waterwheel
01:14:11 -
MAE5790-16 waterwheel equations and Lorenz equations
01:12:41 -
MAE5790-17 Chaos in the Lorenz equations
01:16:35 -
MAE5790-18 Strange attractor for the Lorenz equations
01:13:47 -
MAE5790-19 One dimensional maps
01:14:35 -
MAE5790-20 Universal aspects of period doubling
01:11:56 -
MAE5790-21 Feigenbaum’s renormalization analysis of period doubling
01:15:58 -
MAE5790-22 Renormalization: Function space and a hands-on calculation
01:08:32 -
MAE5790-23 Fractals and the geometry of strange attractors
01:04:32 -
MAE5790-24 Hénon map
51:24 -
MAE5790-25 Using chaos to send secret messages
01:05:21
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