This course on Nonlinear Dynamics and Chaos aims to introduce newcomers to the field by emphasizing analytical methods, concrete examples, and geometric intuition. The course covers topics such as bifurcations, limit cycles, chaos, fractals, and strange attractors, with a focus on applications in various fields. The essential prerequisite for this course is single-variable calculus, with some sections requiring multivariable calculus and linear algebra. The teaching method includes lectures, mathematical theory development, computer graphics, simulations, and demonstrations of nonlinear phenomena. The intended audience for this course includes individuals with a background in calculus and introductory physics who are interested in exploring the fascinating world of nonlinear dynamics and chaos.
Overview
Syllabus
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.
Taught by
Cornell MAE
