Nonlinear Dynamics and Chaos

Explore nonlinear dynamics and chaos through a comprehensive series of 25 lectures filmed at Cornell University in Spring 2014. Delve into analytical methods, concrete examples, and geometric intuition as you progress from first-order differential equations to complex topics like the Lorenz equations, chaos, and strange attractors. Apply theoretical concepts to real-world scenarios, including airplane wing vibrations, biological rhythms, and chaotic waterwheels. Engage with computer graphics, simulations, and videotaped demonstrations to enhance understanding of nonlinear phenomena. Prerequisite knowledge includes single-variable calculus, with some multivariable calculus and linear algebra concepts introduced as needed. Gain insights into the fascinating world of nonlinear systems and their applications across various scientific disciplines.

MAE5790-1 Course introduction and overview.
MAE5790-2 One dimensional Systems.
MAE5790-3 Overdamped bead on a rotating hoop.
MAE5790-4 Model of an insect outbreak.
MAE5790-5 Two dimensional linear systems.
MAE5790-6 Two dimensional nonlinear systems fixed points.
MAE5790-7 Conservative Systems.
MAE5790-8 Index theory and introduction to limit cycles.
MAE5790-9 Testing for closed orbits.
MAE5790-10 van der Pol oscillator.
MAE5790-11 Averaging theory for weakly nonlinear oscillators.
MAE5790-12 Bifurcations in two dimensional systems.
MAE5790-13 Hopf bifurcations in aeroelastic instabilities and chemical oscillators.
MAE5790-14 Global bifurcations of cycles.
MAE5790-15 Chaotic waterwheel.
MAE5790-16 waterwheel equations and Lorenz equations.
MAE5790-17 Chaos in the Lorenz equations.
MAE5790-18 Strange attractor for the Lorenz equations.
MAE5790-19 One dimensional maps.
MAE5790-20 Universal aspects of period doubling.
MAE5790-21 Feigenbaum's renormalization analysis of period doubling.
MAE5790-22 Renormalization: Function space and a hands-on calculation.
MAE5790-23 Fractals and the geometry of strange attractors.
MAE5790-24 Hénon map.
MAE5790-25 Using chaos to send secret messages.