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MAE 5790: Nonlinear Dynamics and Chaos

MAE 5790: Nonlinear Dynamics and Chaos (Spring 2014, Cornell University). Instructor: Professor Steven Strogatz. This course provides an introduction to nonlinear dynamics, with applications to physics, engineering, biology, and chemistry. It closely follows Prof. Strogatz's book, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering."

The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Introduction


Lecture 01 - Course Introduction and Overview
Lecture 02 - One Dimensional Systems
Lecture 03 - Overdamped Bead on a Rotating Hoop
Lecture 04 - Model of an Insect Outbreak
Lecture 05 - Two Dimensional Linear Systems
Lecture 06 - Two Dimensional Nonlinear Systems: Fixed Points
Lecture 07 - Conservative Systems
Lecture 08 - Index Theory and Introduction to Limit Cycles
Lecture 09 - Testing for Closed Orbits
Lecture 10 - Van der Pol Oscillator
Lecture 11 - Averaging Theory for Weakly Nonlinear Oscillators
Lecture 12 - Bifurcations in Two Dimensional Systems
Lecture 13 - Hopf Bifurcations in Aeroelastic Instabilities and Chemical Oscillators
Lecture 14 - Global Bifurcations of Cycles
Lecture 15 - Chaotic Waterwheel
Lecture 16 - Waterwheel Equations and Lorenz Equations
Lecture 17 - Chaos in the Lorenz Equations
Lecture 18 - Strange Attractor for the Lorenz Equations
Lecture 19 - One Dimensional Maps
Lecture 20 - Universal Aspects of Period Doubling
Lecture 21 - Feigenbaum's Renormalization Analysis of Period Doubling
Lecture 22 - Renormalization: Function Space and a Hands-on Calculation
Lecture 23 - Fractals and the Geometry of Strange Attractors
Lecture 24 - Henon Map
Lecture 25 - Using Chaos to Send Secret Messages